Morales-Ramis theorem roughly states as follows: Given an Hamiltonian system, we may linearize it to obtain the variational equation. Then, we associate to the variational equation a group, the differential Galois group. Morales and Ramis have…
Categoria evento: Dynamical Systems Seminar
Normal forms and embedding problem for some formal transseries – Jean-Philippe Rolin (Université de Bourgogne)
Consider a hyperbolic polycycle of an analytic vector field in the real plane. The asymptotic expansion of its first return map is a series whose monomials are products of real powers of the variable and integer powers of its logarithm. Inspired by…
Fixed points, semigroups and rigidity of holomorphic mappings – David Shoikhet (ORT College Braude, Israele)
There is a long history associated with the problem of iterating nonexpansive and holomorphic mappings and finding their fixed points, with the modern results of K. Goebel, W.-A. Kirk, T. Kuczumow, S. Reich, W. Rudin and J.-P. Vigue’ being among the…
On the stability of KAM tori – Bassam Fayad ( CNRS IMJ-PRG e UMI Laboratorio Fibonacci)
Venue Sala Conferenze (Puteano, Centro De Giorgi). Abstract…
Piecewise contractions defined by iterated function systems – Arnaldo Nogueira (Universita’ di Aix Marseille )
We are interested in the asymptotical behavior of piecewise contractions of the interval (PCs). A map $f:[0,1)\to [0,1)$ is an {\it $n$ interval PC} if there exists a partition of the interval $[0,1)$ into subintervals $J_1,\ldots,J_n$ such that…
Metric theory for a new family of continued fraction expansions – Niels Langveld (TU Delft)
The family of flipped expansions and the family of 2-expansions is combined to make a new family of continued fraction expansions we will call flipped 2-expansions. It is shown that there is only one flipped continued fraction expansion map that…
On Kurzweil’s 0-1 Law in Inhomogeneous Diophantine Approximation – Dong Han Kim (Dongguk University)
We give a sufficient and necessary condition such that for almost all $s\in{\mathbb R}$ $$ \ \theta-s\<\psi(n)\qquad\text{for infinitely many}\ n\in{\mathbb N}, $$ where $\theta$ is fixed and $\psi(n)$ is a positive, non-increasing sequence. This…
Misura di Hausdorff di alcune condizioni diofantee e superfici di traslazione. – Luca Marchese (Paris 13)
We consider two dynamical problems for translation surfaces, both related to diophantine approximations: one is the study of the asymptotic amplitude of excursions at infinity of a Teichmuller geodesic in parameter space, the other is the study of…
Continuity of core entropy of quadratic polynomials – Giulio Tiozzo (Yale University)
The core entropy of polynomials, recently introduced by W. Thurston, is a dynamical invariant which can be defined purely in combinatorial terms, and provides a useful tool to study parameter spaces of polynomials. The theory of core entropy extends…
Infinitesimal Hilbert problem – Sergei Yakovenko (Weizmann Institute and Universita di Pisa)
The infinitesimal Hilbert problem addresses limit cycles of planar polynomial vector field, which appear by a small non-conservative perturbation of an integrable (Hamiltonian) system. Their number is closely related to the number of algebraic level…