DinAmicI IX

Contribution List

24. A rigidity result for Kepler billiards

Prof. Vivina Barutello (Università di Torino)

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...

29. Building chaos in billiards with central forces

Prof. Irene De Blasi (Università di Torino)

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...

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

Prof. Sonia Stimac (University of Zagreb, Croatia)

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...

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

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

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...

31. Geometric Properties of Higher Dimensional Solenoidal Attractors

Prof. Daniele Galli (University of Zurich, Switzerland)

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...

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

Prof. Riccardo De Pascalis (Università del Salento)

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...

33. Isoenergetic degeneracy generically creates meandering invariant tori

Prof. Illya Koval (Universität Wien, Austria)

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...

26. Linear response, dicontinuities and holes

Prof. Giovanni Canestrari (University of Toronto, Canada)

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)

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...

44. Synchronization in transformers

Prof. Marco Romito (Università di Pisa)

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.

25. TBA

Prof. Pierre Berger (Université Sorbonne, France)

28. TBA

Prof. Alessandra Celletti (Università di Roma Tor Vergata)

32. TBA

Prof. Marcel Guardia (Universitat de Barcelona, Spain)

34. TBA

Prof. Beatrice Langella (Università di Pisa)

36. TBA

Prof. Iacopo Longo (Imperial College London, UK)

38. TBA

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

41. TBA

Prof. Dario Trevisan (Università di Pisa)

42. TBA

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

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

Prof. Ayreena Bakhtawar (Universität Wien)

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...

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

Prof. Paulo Varandas (Universidade de Aveiro, Portugal)

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...