One-Dimensional Dynamics and High-Dimensional Network Systems
from
Monday, 20 April 2026 (08:00)
to
Friday, 24 April 2026 (22:40)
Monday, 20 April 2026
09:10
Registration
Registration
09:10 - 10:00
Room: Aula Dini
10:00
TBA
-
Stefano Marmi
(
Scuola Normale Superiore
)
TBA
Stefano Marmi
(
Scuola Normale Superiore
)
10:00 - 10:50
Room: Aula Dini
10:50
TBA
-
Weixiao Shen
(
SCMS
)
TBA
Weixiao Shen
(
SCMS
)
10:50 - 11:40
Room: Aula Dini
11:40
Coffee break
Coffee break
11:40 - 12:10
Room: Aula Dini
12:10
Wild Sets with Collet-Eckmann Points and Infinitely Many Sinks:Stability and Coexistence
-
Liviana Palmisano
(
KTH
)
Wild Sets with Collet-Eckmann Points and Infinitely Many Sinks:Stability and Coexistence
Liviana Palmisano
(
KTH
)
12:10 - 13:00
Room: Aula Dini
In two dimensional unfoldings of homoclinic tangencies, the parameter space contains codimension one laminations whose leaves consist of maps with invariant non hyperbolic Cantor sets. I will describe the geometry and dynamics of these Cantor sets. They are wild both in the senses of Hofbauer–Keller and Newhouse, yet contain Collet–Eckmann points with dense orbits. As a consequence, wildness and non uniform chaotic hyperbolicity coexist on a single invariant set and persist along codimension one parameter families. Furthermore, each leaf of the lamination also contains maps with infinitely many sinks accumulating on the Cantor set containing the Collet–Eckmann point. The construction is based on a generalized renormalization scheme for two dimensional systems, which will be outlined in the talk.
14:30
Intermingled basins for skew product systems
-
Ale Jan Homburg
(
University of Amsterdam
)
Intermingled basins for skew product systems
Ale Jan Homburg
(
University of Amsterdam
)
14:30 - 15:20
Room: Aula Dini
In the context of skew product systems, I'll revisit some constructions of maps with multiple attractors that have intermingled basins, and I'll discuss some novel constructions.
15:20
Short Talk: A counterexample to Hölder regularity of the stationary measure for random noninvertible maps.
A counterexample to Hölder regularity of the stationary measure for random noninvertible maps.
15:20 - 15:45
Room: Aula Dini
15:45
Coffee break
Coffee break
15:45 - 16:15
Room: Aula Dini
16:15
Algebraic correspondences: Where rational dynamics meets Kleinian groups- on line talk
-
Luna Lomonaco
(
IMPA
)
Algebraic correspondences: Where rational dynamics meets Kleinian groups- on line talk
Luna Lomonaco
(
IMPA
)
16:15 - 17:05
Room: Aula Dini
The analogies between the iteration of holomorphic maps and the action of Kleinian groups were first systematically explored by Dennis Sullivan in the mid-1980s. In the landmark paper, where he famously proved Fatou's conjecture—that rational maps on the Riemann sphere have no wandering domains—Sullivan introduced what is now known as Sullivan's Dictionary. This conceptual framework draws deep parallels between the definitions, theorems, and conjectures of holomorphic dynamics and those of Kleinian group theory. Sullivan emphasized striking similarities between the Fatou set $F_f$ and Julia set $J_f$ of a holomorphic map $f$ on the Riemann sphere $\widehat{\mathbb{C}}$, and the ordinary set $\Omega(G)$ and limit set $\Lambda(G)$ of a finitely generated Kleinian group $G$ acting on $\widehat{\mathbb{C}}$. His proof of the no wandering domains theorem was directly inspired by methods used to establish Ahlfors’ Finiteness Theorem in the setting of Kleinian groups, highlighting the profound conceptual bridges between the two fields. Both rational maps and finitely generated Kleinian groups can be regarded as special cases of holomorphic correspondences. An $n$-to-$m$ holomorphic correspondence on $\widehat{\mathbb{C}}$ is a multivalued map $\mathcal{F}: z \mapsto w$ defined implicitly by a polynomial relation $P(z, w) = 0$. In 1994, Shaun Bullett and Christopher Penrose introduced the first family of correspondences that contains matings between quadratic rational maps and the modular group, and proved that, for a particular parameter, the correspondence is a mating : it behaves as the modular group on an open subset \Omega, and as a polynomial (and its inverse) in the complement. Since then, the field of correspondences which are matings between rational maps and Kleinian groups grew considerably. In this talk, I will give an overview of the subject.
17:05
Short Talk: Non-statistical skew products with one-dimensional fibers
Non-statistical skew products with one-dimensional fibers
17:05 - 17:30
Room: Aula Dini
Tuesday, 21 April 2026
09:30
Geometry and dynamics of developmental decision making.
-
David Rand
(
University of Warwick
)
Geometry and dynamics of developmental decision making.
David Rand
(
University of Warwick
)
09:30 - 10:20
Room: Aula Dini
I will discuss new work about the use of dynamical systems to understand the early development of an embryo, in particular the way that cells transition from a pluripotent stem cell state to become specialised, complex, functional cells such as neurons, heart cells or the cells in a flower petal. I will describe how a dynamical systems viewpoint leads to new analysis methods for state-of-the-art single-cell data that quantifies the activity of essentially all genes in the cells in a given tissue, such as the early heart. And how ideas from catastrophe and bifurcation theory are used to construct a model of how the cells transition through a complex network of intermediate cells states before adopting their end state. I will also discuss how this leads to new mathematical results and conjectures about how boundary conditions on parameter space force complex bifurcation structures in the interior of the parameter space.
10:20
Universality in Transcendental Dynamics
-
Anna Miriam Benini
(
Università di Parma
)
Universality in Transcendental Dynamics
Anna Miriam Benini
(
Università di Parma
)
10:20 - 11:10
Room: Aula Dini
The Mandelbrot set is a fractal object encoding the dynamical behaviour of the family of quadratic polynomials z^2+c, where c is a parameter varying over the complex plane. It surprisingly appears also in the parameter spaces of all (reasonable) rational maps and in such sense, it also encodes the dynamical behaviour of this much larger class. The explanation is intricate and relies on the concept of renormalization: essentially, renormalization isolates and extrapolates the behaviour of a rational functions near its critical values, and brings it back to analogous behaviours for quadratic polynomials. In this work we present an analogous object for transcendental maps, which arises from a model family and yet encodes the dynamical behaviour of all (reasonable) families of transcendental meromorphic maps. This is joint work with M. Astorg and N. Fagella.
11:10
Coffee break
Coffee break
11:10 - 11:40
Room: Aula Dini
11:40
The Tandelbrot set and the dynamics of tangent-like mappings
-
Núria Fagella
(
Universitat de Barcelona
)
The Tandelbrot set and the dynamics of tangent-like mappings
Núria Fagella
(
Universitat de Barcelona
)
11:40 - 12:30
Room: Aula Dini
The well-know theory of polynomial-like mappings describes the dynamics and bifurcations of proper maps defined in a region containing critical points. If instead we are in a purely transcendental setting, that is, in the presence of an (omitted) asymptotic value and no critical points, we then speak of tangent-like mappings. The model family is known as the generalized tangent family and its bifurcation locus is the boundary of the Tandelbrot set. In this talk we will introduce these concepts and see how they can be used to build a transcendental renormalization theory. This is joint work with Mathieu Astorg and Anna Miriam Benini.
12:30
Short Talk: The Arti-Mazur zeta function for interval maps.
The Arti-Mazur zeta function for interval maps.
12:30 - 12:55
Room: Aula Dini
Contributions
12:30
The Arti-Mazur zeta function for interval maps.
-
Jorge Olivares-Vinales
(
SCMS, Fudan University
)
14:30
Learning network dynamics from data through compressive sensing techniques
-
Edmilson Roque
(
Max Planck Institute, Dresden
)
Learning network dynamics from data through compressive sensing techniques
Edmilson Roque
(
Max Planck Institute, Dresden
)
14:30 - 15:20
Room: Aula Dini
Networks of coupled dynamical systems are fundamental models across the sciences, from physics to neuroscience. Despite their success, the governing equations of such systems are often unknown, limiting our ability to predict and control their dynamics. In many applications, only time series data from the network is accessible, and learning the governing equations from data becomes an inverse problem. In this talk, inspired by compressive sensing techniques, I will show how learning network dynamics from data can be formulated as a convex optimization problem. By exploiting structural information encoded in the network dynamics, such as sparsity, statistical properties, and symmetries, we characterize the minimum amount of data required for learning the network dynamics exactly (and robustly). We illustrate these ideas using networks of coupled chaotic maps and oscillators.
15:20
Short Talk: Adiabatic invariant actions for partially integrable systems
Adiabatic invariant actions for partially integrable systems
15:20 - 15:45
Room: Aula Dini
15:45
Coffee break
Coffee break
15:45 - 16:15
Room: Aula Dini
16:15
Thermodynamics through potential theory- on line talk
-
Fabrizio Bianchi
(
Università di Pisa
)
Thermodynamics through potential theory- on line talk
Fabrizio Bianchi
(
Università di Pisa
)
16:15 - 17:05
Room: Aula Dini
I will describe how tools from potential theory can be used to obtain a very precise statistical description of the dynamics of polynomials and rational maps. In particular, I will explain how the complex setting often allows one to overcome the need for strong a priori hyperbolicity assumptions. This talk is based on joint works with Tien-Cuong Dinh.
17:05
Universal finite-type entire functions
-
Lasse Rempe
(
University of Manchester
)
Universal finite-type entire functions
Lasse Rempe
(
University of Manchester
)
17:05 - 17:55
Room: Aula Dini
A transcendental entire function is said to be of finite type if it has only finitely many critical values (images of critical points) and asymptotic values (non-algebraic singularities of inverse branches). Functions of finite type are of significant interest in complex analysis and complex dynamics. Eremenko and Lyubich showed that the class S of finite-type entire functions is stratified by finite-dimensional complex parameter space, consisting of functions all of which have the same topological mapping behaviour. For example, one such parameter space is given by pre- and post-compositions of the sine function with affine maps. It is a natural question what can happen as functions in a given parameter space degenerate. For example, what are the possible limits of a sequence of functions in such a parameter space that leaves any compact subset thereof? In joint work with Prochorov, we show that this limiting behaviour can be extremely complicated. In fact, we show that, for any given finite set S, there exists a universal function for this set: A transcendental entire function f such that the possible pre-compositions of f with affine maps accumulate on all entire functions with the same singular values. In particular, the parameter space of such a universal function f accumulates on all Moreover, using Bishop's technique of quasiconformal folding, we show that the pre-compositions in question accumulate even on every (not necessarily entire) finite-type map defined on a simply-connected domain and having singular set S. Given time, I will discuss consequences of this result for transcendental dynamics, in particular for the important problem of extending Thurston's characterisation of post-critically finite rational maps to the setting of transcendental dynamics.
20:00
SOCIAL DINNER-- La Pergoletta
SOCIAL DINNER-- La Pergoletta
20:00 - 22:00
Wednesday, 22 April 2026
10:20
IETs rotation numbers and rigidity
-
Corinna Ulcigrai
(
Universität Zürich
)
IETs rotation numbers and rigidity
Corinna Ulcigrai
(
Universität Zürich
)
10:20 - 11:10
Room: Aula Dini
Rigidity is a central question investigated in one dimensional dynamics: we say that a class of one dimensional maps is rigid when a topological conjugacy between two of them has automatically further regularity properties. In this talk we want to highlight how a notion of 'combinatorial rotation number' borrowed from the study of Interval exchange transformations (IETs) can help investigate rigidity in different settings, by discussing two recent results for multi-critical circle maps and affine interval exchange maps (AIETs) respectively. For multi-critical circle maps, assuming exponential convergence of renormalization, we show that two maps with the same signature, under a full measure condition of the latter, are C^(1+a) conjugated (joint work with Estevez and Trujillo). In the setting of AIETs, we describe a class of AIETs which are C^10 but not C^1 conjugated (joint work with Trujillo). In both works, a crucial role in the proofs is played by suitable 'Diophantine-like' conditions (on the signature, or on the IET rotation number) which control combinatorics and exploits the classical Rauzy-Veech induction for IETs.
11:10
Coffee break
Coffee break
11:10 - 11:40
Room: Aula Dini
11:40
Dynamics in the real world.
-
Marco Martens
(
Stony Brook University
)
Dynamics in the real world.
Marco Martens
(
Stony Brook University
)
11:40 - 12:30
Room: Aula Dini
An experiment in cell biology inspired a general method to use the tools/ideas from the theory for dynamical systems to build models for real world processes.
12:30
Short Talk: Smooth Circle Covering with a Physical Measure on a Hyperbolic Repelling Fixed Point
Smooth Circle Covering with a Physical Measure on a Hyperbolic Repelling Fixed Point
12:30 - 12:55
Room: Aula Dini
Contributions
12:30
Smooth Circle Covering with a Physical Measure on a Hyperbolic Repelling Fixed Point
-
Rubio Gunawan The
(
SISSA
)
14:30
Teichmüller spaces and normal forms for wandering domains- on line talk
-
Leticia Pardo Simon
(
Universitat de Barcelona
)
Teichmüller spaces and normal forms for wandering domains- on line talk
Leticia Pardo Simon
(
Universitat de Barcelona
)
14:30 - 15:20
Room: Aula Dini
Wandering domains of entire functions exhibit a wide range of dynamical behaviour, and a useful way to study this is through the associated dynamical Teichmüller space T(U,f). In this talk, I will discuss how the structure of this space depends on the grand orbit relation in the wandering domain. I will show that if the grand orbit relation is discrete, then T(U,f) is infinite-dimensional, answering a question of Fagella–Henriksen. I will then present normal forms for the dynamics on wandering domains, giving global linearising coordinates in the discrete case and power-like dynamics between annuli in the indiscrete case. This is joint work with N. Fagella and G. R. Ferreira.
15:20
Short Talk: Dynamics of Solutions to Quadratic Forms on $\mathbb{R}^3$
Dynamics of Solutions to Quadratic Forms on $\mathbb{R}^3$
15:20 - 15:45
Room: Aula Dini
Contributions
15:20
Dynamics of Solutions to Quadratic Forms on $\mathbb{R}^3$
-
Alden Paige
(
The University of Manchester
)
15:45
Coffee break
Coffee break
15:45 - 16:15
Room: Chiostra interna
16:15
POSTER SESSION
16:15 - 17:15
Room: Chiostra interna
Thursday, 23 April 2026
09:30
Rigidity and density of hyperbolicity: from polynomials to transcendental maps
-
Kostiantyn Drach
(
CRM-Barcelona
)
Rigidity and density of hyperbolicity: from polynomials to transcendental maps
Kostiantyn Drach
(
CRM-Barcelona
)
09:30 - 10:20
Room: Aula Dini
In this talk, I will introduce a large class of transcendental entire maps to which we can transfer several central results in polynomial dynamics; this includes many of the available results on rigidity and density of hyperbolicity. This transfer is done via our main tool: dynamically meaningful polynomial approximations, which we establish in the near-degenerate regime. If time permits, I will also outline further implications for Transcendental Thurston Theory. Based on joint work, partially in progress, with Dzmitry Dudko.
10:20
A simple model for the population dynamics in OTC wholesale fresh product markets
-
Bastien Fernandez
(
Laboratoire de Probabilités, Statistique et Modélisation
)
A simple model for the population dynamics in OTC wholesale fresh product markets
Bastien Fernandez
(
Laboratoire de Probabilités, Statistique et Modélisation
)
10:20 - 11:10
Room: Aula Dini
The purpose of this talk is to introduce a dynamical model for the time evolution of buyers populations in over-the-counter (OTC) wholesale fresh product markets and to the present the results of its mathematical analysis. The dynamics is governed by immediate reactions of buyers and sellers to changes in basic indicators. Buyers are influenced by some degree of loyalty to their regular suppliers. Yet, at times, they also prospect for better offers. On the other hand, sellers primarily aim at maximising their profit. Yet, they can be also prone to improving their competitiveness in case of clientele deficit. The analysis reveals that the dynamics spontaneously self-regulates in time and generates (transient) oscillatory behaviours that prevent any seller to dominate permanently its competitors (and to be permanently dominated). Long-term behaviours are also investigated, with focus on asymptotic convergence to equilibrium. In particular, in the simplest case of 2 competing sellers, a normal-form-like analysis in the neighbourhood of an elliptic fixed point proves that such convergence holds under suitable, yet economically meaningful, assumptions on the model’s characteristics.
11:10
Coffee break
Coffee break
11:10 - 11:40
Room: Aula Dini
11:40
Lorenz attractor in the Lorenz map
-
Dmitry Turaev
(
Imperial College London
)
Lorenz attractor in the Lorenz map
Dmitry Turaev
(
Imperial College London
)
11:40 - 12:30
Room: Aula Dini
It is known that the dynamics of a Lorenz-like attractor are described by a singular one-dimensional map (the quotient of the Poincare map over the strong-stable invariant foliation). For Lorenz attractors emerging out of a variety of homoclinic bifurcations, this map takes a universal form — it is a C^1-small perturbation of the map X --> |1 - c X^b| where the parameter c can be arbitrary, and 0 < b < 1, so the map has an infinite derivative at zero and positive Schwarzian. We give a complete description of the attractors for this family of maps and for all its low-regularity perturbations. In particular, we determine the region in the parameter plane (b,c) for which the Lyapunov exponent is positive for all orbits. The main difficulty is that for small values of b the map is contracting for long series of consecutive iterations, but we show that the expansion always prevails. This is a joint work with Klim Safonov.
12:30
Short Talk: High order homoclinic tangencies and universal dynamics for multidimensional diffeomorphisms
High order homoclinic tangencies and universal dynamics for multidimensional diffeomorphisms
12:30 - 12:55
Room: Aula Dini
Contributions
12:30
High order homoclinic tangencies and universal dynamics for multidimensional diffeomorphism
-
Dmitrii Mints
(
Imperial College London
)
14:30
Hausdorff measure for continued fraction iterated function system
-
Anna Zdunik
(
Uniwersytet Warszawski
)
Hausdorff measure for continued fraction iterated function system
Anna Zdunik
(
Uniwersytet Warszawski
)
14:30 - 15:20
Room: Aula Dini
15:20
Short Talk: A Tensorization Approach to Overcoming the Curse of Dimensionality in High-Dimensional Coupled Systems
A Tensorization Approach to Overcoming the Curse of Dimensionality in High-Dimensional Coupled Systems
15:20 - 15:45
Room: Aula Dini
Contributions
15:20
A Tensorization Approach to Overcoming the Curse of Dimensionality in High- Dimensional Coupled Systems
-
Giuseppe Tenaglia
(
Imperial college London
)
15:45
Coffee break
Coffee break
15:45 - 16:15
Room: Aula Dini
16:15
The Topological Boshernitzan-Kornfeld Conjecture
-
Leon Staresinic
(
Universität Zürich
)
The Topological Boshernitzan-Kornfeld Conjecture
Leon Staresinic
(
Universität Zürich
)
16:15 - 17:05
Room: Aula Dini
Interval Translations Maps (ITMs) are a natural generalisation of the well-known Interval Exchange Transformations (IETs). They are obtained by dropping the bijectivity assumption for IETs. As such, they are exactly the finite piecewise isometries of the interval. There are two types of ITMs, finite-type and infinite-type ones. They are classified by their non-wandering sets: it is a finite union of intervals for finite-type maps, and contains a Cantor set for infinite-type maps. One of the basic questions in the field is: How prevalent is each type of map in the parameter space? In this work, we show that the set of finite-type maps contains an open and dense subset of the parameter space of ITMs with a fixed number of intervals, which resolves in positive the topological version of a long-standing conjecture due to Boshernitzan and Kornfeld. This is a joint work with Kostiantyn Drach and Sebastian van Strien.
17:05
Equilibrium States for Doubly Intermittent Maps
-
Stefano Luzzatto
(
ICTP
)
Equilibrium States for Doubly Intermittent Maps
Stefano Luzzatto
(
ICTP
)
17:05 - 17:55
Room: Aula Dini
We study the existence and uniqueness of equilibrium states for various potentials for a class of doubly intermittent maps. This is joint work with J.Alves, V. Ramos and J. Siqueira.
Friday, 24 April 2026
09:30
Ergodic properties of sums of visits to $[0,1/2)$ by quadratic irrational rotations.
-
Henk Bruin
(
University of Vienna
)
Ergodic properties of sums of visits to $[0,1/2)$ by quadratic irrational rotations.
Henk Bruin
(
University of Vienna
)
09:30 - 10:20
Room: Aula Dini
The visit sums and averages of orbits under irrational rotations has been of interest since at least the seminal work of Kesten in the 1960. Recent work by Avila et al. revisted the problem in the case that the rotation number is a quadratic irrational, showing that the typical behaviour is slightly different from what Kesten proved for typical rotation numbers. Their method is based on $\Z$-extension (skew-products) over the rotation and certain renormalization techniques. We recently generalized their method so as to include samples of Ehrenfest wind-tree model as well. Using purely combinatoric methods, it is possible to give precise statements about visit sums for particular orbits, or actually the orbit of 0. This orbit is actually non-typical in view to the results of Avila et al. The talk is based on joint work with Charles Fourgeron, Davide Ravotti, Dalia Terhesiu, and with Robert Fokkink.
10:20
Mixing and ergodicity of non-autonomous circle dynamics
-
Gustavo Rodrigues Ferreira
(
Centre de Recerca Matemàtica
)
Mixing and ergodicity of non-autonomous circle dynamics
Gustavo Rodrigues Ferreira
(
Centre de Recerca Matemàtica
)
10:20 - 11:10
Room: Aula Dini
Thanks to the work of Aaronson, Doering and Mañé, Craizer, and many others, we know that the properties of an inner function and its dynamics in the unit disc are closely related to the dynamics of its boundary extension. If, however, we consider compositions of inner functions, i.e. non-autonomous dynamics in the unit disc, less is known about its relation to the corresponding non-autonomous dynamical system on the unit circle given by composing the boundary extensions. In this talk, we will tackle this problem from the point of view of ergodic theory. We will discuss necessary and sufficient conditions for mixing and ergodicity, construct examples and counterexamples, and present some consequences of ergodicity. This is joint work with Artur Nicolau (UAB).
11:10
coffee break
coffee break
11:10 - 11:40
Room: Aula Dini
11:40
Short Talk: Reconstructing resonant phase oscillator interactions from noisy time series
Reconstructing resonant phase oscillator interactions from noisy time series
11:40 - 12:05
Room: Aula Dini
12:05
Revealing Dynamics, Communities, and Criticality from Data
-
Tiago Pereira
(
Universidade de São Paulo
)
Revealing Dynamics, Communities, and Criticality from Data
Tiago Pereira
(
Universidade de São Paulo
)
12:05 - 12:30
Room: Aula Dini
Complex systems consist of interacting units connected through intricate networks. Predicting sudden changes in their dynamics is essential to mitigate the consequences of large-scale disruptions. This task is inherently challenging, as it requires forecasting behavior in parameter regimes where no data are available. We address this problem for networks with chaotic local dynamics by reconstructing both the individual dynamics and a statistical description of their interactions directly from data. We show that the network behavior admits a decomposition into an emergent deterministic component and a fluctuation term. While such fluctuations are traditionally treated as noise and filtered out, we demonstrate that they are in fact essential for uncovering the underlying interaction structure such as community structures. This enables the early prediction of synchronization transitions in networks with community structure, even when the system operates far from the transition regime.
12:30
TBA
-
Jeroen Lamb
(
Imperial College London
)
TBA
Jeroen Lamb
(
Imperial College London
)
12:30 - 13:00
Room: Aula Dini