DinAmicI IX

Contribution List

25. Wild dynamics on manifold

Prof. Pierre Berger (Université Sorbonne, France)

19/10/2026, 09:30

We survey a few results on differentiable, symplectic, or analytic wild dynamics.

43. When Contraction Is Not Enough: Symbolics, endpoints and (in)stability of local IFSs

Prof. Paulo Varandas (Universidade de Aveiro, Portugal)

19/10/2026, 10:20

Classical contractive iterated function (IFSs) systems enjoy a remarkably rigid picture: a unique attractor, full symbolic coding, and robust asymptotic behavior. This picture changes substantially when the maps are defined only on prescribed local domains. In this talk, we present a framework for contractive local iterated function systems and investigate the structure and stability of their...

28. Ring's dynamics: from KAM to bifurcation theory

Prof. Alessandra Celletti (Università di Roma Tor Vergata)

19/10/2026, 11:40

This talk presents a Hamiltonian framework for modelling the dynamics of ring particles orbiting celestial bodies, encompassing both nearly spherical planets and markedly non-spherical asteroids. The Hamiltonian is formulated using the so-called epicyclic variables. The subsequent analysis focuses on the dynamics in the vicinity of resonances, specifically on commensurabilities between the...

44. Synchronization in transformers

Prof. Marco Romito (Università di Pisa)

19/10/2026, 14:30

The first part of the talk will introduce a mathematical framework for transformers architectures, focusing in particular on how information travels through the layers of the network. In the second part we will briefly discuss infinite-width, infinite-depth and infinite-tokens limits. Finally, the third part will focus on synchronization and some noise-induced phenomena.

42. The Thurston algorithm for real entire transcendental post-singularly finite maps

Prof. Sebastian van Strien (Imperial College London, UK)

19/10/2026, 15:50

Thurston’s characterisation theorem gives a necessary and sufficient condition for when a branched covering map of the sphere (for which the orbits of the branch points have finite cardinality) can be realised by a rational map. In spite of progress, an analogous result for entire maps of the complex plane seem to be not yet known. In this talk, I will discuss a different approach in the...

38. Trimmed sums, extravagances and extreme historic behaviour

Prof. Tanja I. Schindler (University of Exeter, UK)

19/10/2026, 16:40

We consider an irrational rotation R_α on the torus (R_α(x)= x+α mod 1) and the non-integrable observable f(x)=1/x-1/(1-x) and study the Birkhoff sum S_n=f+...+f(R_α^(n-1)). As by Aaronson's theorem it is not possible to obtain strong convergence for S_n/d_n where d_n is any norming sequence, we look at the trimmed sum where we delete one or more of the maximal terms to obtain strong...

32. Partially hyperbolic dynamics in the 3-body problem

Prof. Marcel Guardia (Universitat de Barcelona, Spain)

20/10/2026, 09:30

In this talk I will explain how to construct symplectic blenders for two classical Hamiltonian systems: the 3-body problem and its restricted version. These objects lead to a strong form of topological instability. This is a joint work with Jaime Paradela.

40. Classification of Henon maps with strange attractors via a stable manifold

Prof. Sonia Stimac (University of Zagreb, Croatia)

20/10/2026, 10:20

In an earlier work with Boronski, we classified (up to conjugacy) the Henon maps with strange attractors in terms of three invariants that we introduced for them: (a) kneading sequences, (b) pruned trees, and (c) folding patterns of the unstable manifold of the hyperbolic fixed point $X$ in the attractor.
In my talk, I will introduce yet another way to determine conjugacy classes of these...

41. Wide Deep Neural Networks as Random Dynamical Systems: From Gaussian Limits to Least Action

Prof. Dario Trevisan (Università di Pisa)

20/10/2026, 11:40

Wide fully connected neural networks admit a remarkably tractable probabilistic description at large width. At fixed depth, their outputs converge to Gaussian processes, while the empirical covariance kernels of successive layers evolve according to a deterministic nonlinear recursion. Interpreting depth as a discrete time variable, this places the standard neural-network Gaussian process...

30. Identifying Almost-Invariant Regions in Space Debris Dynamics via Transfer Operators

Prof. Riccardo De Pascalis (Università del Salento)

20/10/2026, 14:30

In recent years, techniques from ergodic theory have been successfully applied to investigate a wide range of real-world phenomena. In this work, we explore how the spectral properties of transfer operators can provide insight into transport in space debris dynamics, with the aim of identifying regions that resist mixing over long timescales.

We consider an ensemble of small orbiting debris...

34. Nekhoroshev Theorem for time quasiperiodic perturbations of integrable systems

Prof. Beatrice Langella (Università di Pisa)

20/10/2026, 15:50

Consider a small amplitude perturbation of an analytic integrable Hamiltonian system: Nekhoroshev theorem ensures that, if the unperturbed part of the Hamiltonian fulfills a suitable non-degeneracy assumption, known in literature as steepness, all the actions are quasi-preserved for time scales that are exponentially long in the perturbative parameter.
What happens when the perturbative term...

31. Geometric Properties of Higher Dimensional Solenoidal Attractors

Prof. Daniele Galli (University of Zurich, Switzerland)

21/10/2026, 09:30

We study the skew product systems $T:\mathbb{S}^1\times\mathbb{R}^d\to\mathbb{S}^1\times\mathbb{R}^d$, $T(x,y)=(\ell x, A y+\phi(x)),$ where $\ell\geq 2,$ $A \in GL_d(\mathbb{R})$, with $\rho(A)<1$, and $\phi \in C^r(\mathbb{S}^1, \mathbb{R}^d)$. We show that for a generic $\phi$:
if $|\det(A)|\ell<1$, the Hausdorff dimension of the solenoid attractor and the SRB measure dimension equals the...

36. Nonautonomous differential equations in the presence of bounded noise

Prof. Iacopo Longo (Imperial College London, UK)

21/10/2026, 10:20

Nonautonomous systems subject to noise arise naturally in many applied contexts. Particularly relevant are those featuring time-dependent parameters and uncertainties, which may drive the emergence of tipping points. In this talk, we focus on the case of bounded noise, where the dynamics can be captured topologically via deterministic set-valued dynamical systems: initial conditions are...

29. Building chaos in billiards with central forces

Prof. Irene De Blasi (Università di Torino)

21/10/2026, 11:40

In recent years, a large community of mathematicians has become increasingly interested in the study of billiards with potential, investigating how the transition from straight geodesics to curved ones can influence the overall dynamics. In particular, the presence of singularities can greatly enrich the dynamics, leading to chaotic phenomena not observed in the case of classical billiards. In...

24. A rigidity result for Kepler billiards

Prof. Vivina Barutello (Università di Torino)

21/10/2026, 14:30

We study the integrability of Kepler billiards, mechanical systems in which a particle moves under the influence of a Keplerian potential and undergoes elastic reflections at the boundary of a strictly convex planar domain with smooth boundary. We prove that, with the possible exception of a single position of the gravitational center, analytic integrability at any energy regime can occur...

26. Linear response, dicontinuities and holes

Prof. Giovanni Canestrari (University of Toronto, Canada)

21/10/2026, 15:50

Linear response means that the equilibrium measures of chaotic dynamical systems react to perturbations linearly in the perturbation strength. After reviewing some obstructions to linear response for 1D expanding maps, I will present some results on linear response for discontinuous perturbations and systems with holes in higher dimensions.

27. Mean-field derivation of a Vlasov-type equation in a Sinai billiard

Prof. Roberto Castorrini (Università della Tuscia)

21/10/2026, 16:40

We study a system of mean-field coupled particles moving in a Sinai billiard under the influence of an electric field and a Gaussian thermostat, together with the associated nonlinear Vlasov-type equation. We prove existence and uniqueness of the macroscopic evolution through a fixed-point formulation involving self-consistent transfer operators, and show that it arises as the mean-field limit...

35. Extreme Value Theorem for geodesic flow on the quotient of the theta group

Dr Seul Bee Lee (Seoul National University, South Korea)

22/10/2026, 09:30

The extreme value theorem (EVT) is a theory concerning the distribution of the maximum of a sequence of random variables. For classical continued fractions, an EVT has been established, describing the limiting distribution of large partial quotients. Their significance is further explained by the correspondence with geodesic flow on the modular surface, where large partial quotients can be...

23. Weighted Products of Digits in Gauss-like Iterated Function Systems

Prof. Ayreena Bakhtawar (Universität Wien)

22/10/2026, 10:20

The growth of continued-fraction digits is closely related to Diophantine approximation. Products of consecutive digits arise, in particular, in questions concerning improvements to Dirichlet’s theorem. These connections motivate the study of the Hausdorff dimension of sets defined by prescribed growth of digit products.
In this talk, I will discuss weighted products of digits in d-decaying...

33. Isoenergetic degeneracy generically creates meandering invariant tori

Prof. Illya Koval (Universität Wien, Austria)

22/10/2026, 11:40

Consider the set of isoenergetically degenerate integrable Hamiltonians with two degrees of freedom. We show that a cusp-generic perturbation of a generic Hamiltonian in this set gives rise to meandering invariant tori - embedded Lagrangian tori which are not graphs. Moreover, an exponentially dense subset of perturbations admits higher order meandering tori, of all orders from two to...