Continuity of topological entropy for perturbation of time-one maps of hyperbolic flows

Radu Saghin; Jiagang Yang

doi:10.1007/s11856-016-1396-4

Continuity of topological entropy for perturbation of time-one maps of hyperbolic flows

Radu Saghin, Jiagang Yang

INSTITUTE OF MATHEMATICS

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11 Scopus citations

Abstract

We consider a C¹ neighborhood of the time-one map of a hyperbolic flow and prove that the topological entropy varies continuously for diffeomorphisms in this neighborhood. This shows that the topological entropy varies continuously for all known examples of partially hyperbolic diffeomorphisms with one-dimensional center bundle.

Original language	English
Pages (from-to)	857-875
Number of pages	19
Journal	Israel Journal of Mathematics
Volume	215
Issue number	2
DOIs	https://doi.org/10.1007/s11856-016-1396-4
State	Published - 1 Sep 2016

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title = "Continuity of topological entropy for perturbation of time-one maps of hyperbolic flows",

abstract = "We consider a C1 neighborhood of the time-one map of a hyperbolic flow and prove that the topological entropy varies continuously for diffeomorphisms in this neighborhood. This shows that the topological entropy varies continuously for all known examples of partially hyperbolic diffeomorphisms with one-dimensional center bundle.",

author = "Radu Saghin and Jiagang Yang",

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AB - We consider a C1 neighborhood of the time-one map of a hyperbolic flow and prove that the topological entropy varies continuously for diffeomorphisms in this neighborhood. This shows that the topological entropy varies continuously for all known examples of partially hyperbolic diffeomorphisms with one-dimensional center bundle.

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Continuity of topological entropy for perturbation of time-one maps of hyperbolic flows

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