Symbolic extensions for 3-dimensional diffeomorphisms

David Burguet; Gang Liao

doi:10.1007/s11854-021-0185-0

Symbolic extensions for 3-dimensional diffeomorphisms

David Burguet
, Gang Liao

École Polytechnique

Soochow University

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that every C^r diffeomorphism with r > 1 on a three-dimensional manifold admits symbolic extensions, i.e., topological extensions which are subshifts over a finite alphabet. This answers positively a conjecture of Downarowicz and Newhouse in dimension three.

Original language	English
Pages (from-to)	381-400
Number of pages	20
Journal	Journal d'Analyse Mathematique
Volume	145
Issue number	1
DOIs	https://doi.org/10.1007/s11854-021-0185-0
Publication status	Published - 1 Dec 2021

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abstract = "We prove that every Cr diffeomorphism with r > 1 on a three-dimensional manifold admits symbolic extensions, i.e., topological extensions which are subshifts over a finite alphabet. This answers positively a conjecture of Downarowicz and Newhouse in dimension three.",

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Symbolic extensions for 3-dimensional diffeomorphisms

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