In this talk, I will discuss a shrinking target problem in the space of uni-modular lattices, with target located at infinity and shrinking neighbourhoods determined by the injectivity radius function. This problem is connected to a large body of…
Categoria evento: Dynamical Systems Seminar
Upper bound on the regularity of Lyapunov exponents of random product of matrices – Jamerson Bezerra (Nicolaus Copernicus University)
The study of the regularity of the Lyapunov exponent of random products of SL2(R) matrices is a rich subject with many important contributions in the past years. It is well established in the literature that the function which associates each finite…
Random iteration on hyperbolic Riemann surfaces – Marco Abate (University of Pisa)
In this talk we shall describe the asymptotic behaviour of sequences of functions obtained by iteratively left-composing or right-composing holomorphic self-maps of a hyperbolic Riemann surface $X$. We shall consider in detail two cases: when the…
Strong limit theorems for infinite measure-preserving dynamical systems with applications to non-standard continued fraction algorithms – Tanja Schindler (Univ. of Wien)
Aaronson’s theorem states that if we have a non-integrable observable over a finite measure system or if we have an integrable observable over a infinite measure space, then in both cases we can not have a strong law of large numbers. However -…
Renormalization of analytic maps of the annulus and applications to conjugacy problems – Michael Yampolsky (Univ. of Toronto)
In a recent series of works with N. Goncharuk, we have constructed an analytic renormalization operator acting on conformal maps of the annulus. We showed that this operator has a hyperbolic horseshoe attractor consisting of Brjuno rotations. I will…
On the infinite dimension limit of invariant measures and solutions of Zeitlin’s 2D Euler equations – Milo Viviani (SNS)
In this talk we consider a finite dimensional approximation for the 2D Euler equations on the sphere, proposed by V. Zeitlin, and show their convergence towards a solution of the Euler equations with marginals distributed as the enstrophy measure.…
Recurrence for smooth curves in the moduli space of translation surfaces – Krzysztof Frączek
My talk is a kind of review of problems and recent results regarding smooth curves in the moduli space of translation surfaces and Teichmüller positive semi-orbits starting from such curves. I plan to present some abstract results about the…
Attractors of dual continued fractions – Giovanni Panti
Given a Farey-type map F with full branches in the extended Hecke group Gamma_m, its dual F_# results from constructing the natural extension of F, letting time go backwards, and projecting. Although numerical simulations may suggest otherwise, we…
Horocycle flows on Abelian covers of hyperbolic surfaces – Davide Ravotti (Universität Wien)
The horocycle flow on the unit tangent bundle of a surface of constant negative curvature is the unit speed translation…
Limit Theorems for a class of unbounded observables on the real line with an application to sampling the Lindelöf Hypothesis – Kasun Fernando (Centro De Giorgi – SNS)
We prove the Central Limit Theorem, first order Edgeworth expansion and Mixing Local Limit Theorem for the Birkhoff sums of a class of L^3 observables over Boolean-type transformations on the real line. The class of observables include the real…