One-Dimensional Dynamics and High-Dimensional Network Systems

Contribution List

15. TBA

Stefano Marmi (Scuola Normale Superiore)

20/04/2026, 10:00

30. TBA

Weixiao Shen (SCMS)

20/04/2026, 10:50

24. Wild Sets with Collet-Eckmann Points and Infinitely Many Sinks:Stability and Coexistence

Liviana Palmisano (KTH)

20/04/2026, 12:10

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...

35. Intermingled basins for skew product systems

Ale Jan Homburg (University of Amsterdam)

20/04/2026, 14:30

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.

21. Algebraic correspondences: Where rational dynamics meets Kleinian groups- on line talk

Luna Lomonaco (IMPA)

20/04/2026, 16:15

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...

26. Geometry and dynamics of developmental decision making.

David Rand (University of Warwick)

21/04/2026, 09:30

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...

17. Universality in Transcendental Dynamics

Anna Miriam Benini (Università di Parma)

21/04/2026, 10:20

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...

20. The Tandelbrot set and the dynamics of tangent-like mappings

Núria Fagella (Universitat de Barcelona)

21/04/2026, 11:40

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...

39. The Arti-Mazur zeta function for interval maps.

Jorge Olivares-Vinales (SCMS, Fudan University)

21/04/2026, 12:30

Short Talk

In this talk, I will discuss recent work characterizing the rationality of the Artin–Mazur zeta function for unimodal maps. I will then present examples showing that this characterization fails for multimodal maps, and therefore for polynomial maps of higher degree. If time permits, I will also explain how these examples connect to Thurston’s conjecture on the structure of isentropes for...

29. Learning network dynamics from data through compressive sensing techniques

Edmilson Roque (Max Planck Institute, Dresden)

21/04/2026, 14:30

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...

18. Thermodynamics through potential theory- on line talk

Fabrizio Bianchi (Università di Pisa)

21/04/2026, 16:15

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.

27. Universal finite-type entire functions

Lasse Rempe (University of Manchester)

21/04/2026, 17:05

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...

32. IETs rotation numbers and rigidity

Corinna Ulcigrai (Universität Zürich)

22/04/2026, 10:20

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...

23. Dynamics in the real world.

Marco Martens (Stony Brook University)

22/04/2026, 11:40

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.

43. Smooth Circle Covering with a Physical Measure on a Hyperbolic Repelling Fixed Point

Rubio Gunawan The (SISSA)

22/04/2026, 12:30

Short Talk

We construct an example of a smooth circle covering map topologically conjugate to the doubling map, such that it has a physical measure supported on a hyperbolic repelling fixed point. By relaxing the smooth condition at a single point, we also construct an example where the basin of the physical measure has full measure. A key technical step is a realization lemma of independent interest,...

45. Teichmüller spaces and normal forms for wandering domains- on line talk

Leticia Pardo Simon (Universitat de Barcelona)

22/04/2026, 14:30

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,...

40. Dynamics of Solutions to Quadratic Forms on $\mathbb{R}^3$

Alden Paige (The University of Manchester)

22/04/2026, 15:20

Short Talk

It is known that every positive primitive Pythagorean triple can be uniquely express in the form $M_{a_1} \ldots M_{a_n} v$, where each $M_{a_i}$ is one of three specific matrices, and $v$ is either $(3,4,5)^T$ or $(4,3,5)^T$. Motivated by a desire to compute this code for any given triple, Romik presented an ergodic dynamical system on the positive quadrant of the unit circle, and conjugated...

19. Rigidity and density of hyperbolicity: from polynomials to transcendental maps

Kostiantyn Drach (CRM-Barcelona)

23/04/2026, 09:30

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...

22. A simple model for the population dynamics in OTC wholesale fresh product markets

Bastien Fernandez (Laboratoire de Probabilités, Statistique et Modélisation)

23/04/2026, 10:20

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...

34. Lorenz attractor in the Lorenz map

Dmitry Turaev (Imperial College London)

23/04/2026, 11:40

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...

38. High order homoclinic tangencies and universal dynamics for multidimensional diffeomorphism

Dmitrii Mints (Imperial College London)

23/04/2026, 12:30

Short Talk

Our research is aimed at studying the dynamics of smooth multidimensional diffeomorphisms from the Newhouse domain, that is, open regions in the space of maps where systems with homoclinic tangencies are dense. We prove that in the space of smooth and real-analytic multidimensional maps in any neighborhood of a map such that it has a bi-focus periodic orbit whose invariant manifolds are...

33. Hausdorff measure for continued fraction iterated function system

Anna Zdunik (Uniwersytet Warszawski)

23/04/2026, 14:30

42. A Tensorization Approach to Overcoming the Curse of Dimensionality in High- Dimensional Coupled Systems

Giuseppe Tenaglia (Imperial college London)

23/04/2026, 15:20

Short Talk

Perturbations of high-dimensional systems are notoriously delicate: even when their magnitude vanishes with the dimension, their cumulative effect may remain significant due to the curse of dimensionality.
We study a class of uncoupled noisy systems perturbed by the introduction of a hole whose size decreases as the dimension grows. Although the perturbation becomes asymptotically small, its...

31. The Topological Boshernitzan-Kornfeld Conjecture

Leon Staresinic (Universität Zürich)

23/04/2026, 16:15

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...

11. Equilibrium States for Doubly Intermittent Maps

Stefano Luzzatto (ICTP)

23/04/2026, 17:05

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.

12. Ergodic properties of sums of visits to $[0,1/2)$ by quadratic irrational rotations.

Henk Bruin (University of Vienna)

24/04/2026, 09:30

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...

28. Mixing and ergodicity of non-autonomous circle dynamics

Gustavo Rodrigues Ferreira (Centre de Recerca Matemàtica)

24/04/2026, 10:20

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...

16. Revealing Dynamics, Communities, and Criticality from Data

Tiago Pereira (Universidade de São Paulo)

24/04/2026, 11:40

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...

14. TBA

Jeroen Lamb (Imperial College London)

24/04/2026, 14:30

37. A counterexample to Hölder regularity of the stationary measure for random noninvertible maps.

Vincent Goverse (Imperial College London)

Short Talk

Gorodetski, Kleptsyn, and Monakov [1] recently proved that for random dynamical systems on compact Riemannian manifolds generated by bi-Lipschitz homeomorphisms, the stationary measure is Hölder regular whenever the maps do not share a common invariant measure. In this talk, we show that this result does not extend to noninvertible, locally Lipschitz maps. We construct an explicit...

44. Adiabatic invariant actions of partially integrable systems

Amir Khodaeian Karim (Imperial college)

Short Talk

We introduce action variables for partially integrable systems. We prove that for slow-fast partially integrable Hamiltonian systems, when the restriction of the Hamiltonian to the common level of the integrals is ergodic, a slow change of parameters creates geometrically defined adiabatic invariants that are integrals of the averaged system. This is in contrast to the absence of ergodcity....

41. Non-statistical skew products with one-dimensional fibers

Raul Steven Rodriguez Chavez (ICTP and PUC-Rio)

Short Talk

We study the occurrence of non-statistical behavior for almost every point in the setting of skew products with one-dimensional fiber dynamics. Under suitable ergodic conditions, we establish that a weak form of the arcsine law leads to the non-convergence of Birkhoff averages along almost every orbit. As an application, we show that this phenomenon occurs for one-step skew product maps over a...

47. Reconstructing resonant phase oscillator interactions from noisy time series

Bengi Dönmez (Vrije Universiteit Amsterdam)

Short Talk

We present a novel method for reconstructing networks and hypernetworks of coupled phase oscillators from noisy time series. Noise and uncertainty can make it hard or impossible to distinguish different oscillator networks based on observed dynamical behavior. Thus, our method does not aim to determine exact phase equations for the oscillators, but instead recovers their first and second order...