Zobrazeno 1 - 10
of 99
pro vyhledávání: '"Katok, Anatole"'
Autor:
Katok, Anatole, Krikorian, Raphaël
Let $f$ be a smooth symplectic diffeomorphism of $\mathbb{R}^2$ admitting a (non-split) separatrix associated to a hyperbolic fixed point. We prove that if $f$ is a perturbation of the time-1 map of a symplectic autonomous vector field, this separatr
Externí odkaz:
http://arxiv.org/abs/2109.10137
Measure-theoretic and topological entropy are classical invariants in the theory of dynamical systems. There are several recently developed entropy type invariants for systems of sub-exponential growth: sequence entropy, slow entropy, Kakutani invari
Externí odkaz:
http://arxiv.org/abs/2004.04655
We outline the flexibility program in smooth dynamics, focusing on flexibility of Lyapunov exponents for volume-preserving diffeomorphisms. We prove flexibility results for Anosov diffeomorphisms admitting dominated splittings into one-dimensional bu
Externí odkaz:
http://arxiv.org/abs/1908.07891
Autor:
Erchenko, Alena, Katok, Anatole
We consider a smooth closed surface $M$ of fixed genus $\geqslant 2$ with a Riemannian metric $g$ of negative curvature with fixed total area. The second author has shown that the topological entropy of geodesic flow for $g$ is greater than or equal
Externí odkaz:
http://arxiv.org/abs/1710.00079
We consider two numerical entropy--type invariants for actions of $\Zk$, invariant under a choice of generators and well-adapted for smooth actions whose individual elements have positive entropy. We concentrate on the maximal rank case, i.e. $\Zk,\,
Externí odkaz:
http://arxiv.org/abs/1311.0927
Autor:
Fayad, Bassam, Katok, Anatole
We construct examples of volume-preserving uniquely ergodic (and hence minimal) real-analytic diffeomorphisms on odd-dimemsional spheres
Externí odkaz:
http://arxiv.org/abs/1309.3137
We prove that any smooth action of $\mathbb Z^{m-1}, m\ge 3$ on an $m$-dimensional manifold that preserves a measure such that all non-identity elements of the suspension have positive entropy is essentially algebraic, i.e. isomorphic up to a finite
Externí odkaz:
http://arxiv.org/abs/1305.7262
Autor:
Climenhaga, Vaughn, Katok, Anatole
These expository notes are a somewhat embellished version of two rather informal evening review sessions given by the second author at the 2008 Bedlewo summer school on "Dynamical Systems - Geometric Structures and Rigidity"; they provide a brief ove
Externí odkaz:
http://arxiv.org/abs/1208.4550
We prove that any real-analytic action of $SL(n,\Z), n\ge 3$ with standard homotopy data that preserves an ergodic measure $\mu$ whose support is not contained in a ball, is analytically conjugate on an open invariant set to the standard linear actio
Externí odkaz:
http://arxiv.org/abs/1002.2942