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pro vyhledávání: '"Katok, A."'
We study the topological entropy of a two-parameter family of maps related to (a,b)-continued fraction algorithms and prove that it is constant on a square within the parameter space (two vertices of this square correspond to well-studied continued f
Externí odkaz:
http://arxiv.org/abs/2210.07389
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
Given a closed, orientable surface of constant negative curvature and genus $g \ge 2$, we study the topological entropy and measure-theoretic entropy (with respect to a smooth invariant measure) of generalized Bowen--Series boundary maps. Each such m
Externí odkaz:
http://arxiv.org/abs/2106.13779
Given a closed, orientable surface of constant negative curvature and genus $g \ge 2$, we study a family of generalized Bowen-Series boundary maps and prove the following rigidity result: in this family the topological entropy is constant and depends
Externí odkaz:
http://arxiv.org/abs/2101.10271
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
Akademický článek
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Given a closed, oriented, compact surface $S$ of constant negative curvature and genus $g \ge 2$, we study the measure-theoretic entropy of the Bowen-Series boundary map with respect to its smooth invariant measure. We obtain an explicit formula for
Externí odkaz:
http://arxiv.org/abs/1909.07032