Symbolic extensions in intermediate smoothness on surfaces

IF 1.3 1区数学 Q1 MATHEMATICS

Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2011-03-30 DOI:10.24033/ASENS.2167

David Burguet

引用次数: 16

Abstract

We prove that $\mathcal{C}^r$ maps with $r>1$ on a compact surface have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. More precisely we give a sharp upper bound on the so-called symbolic extension entropy, which is the infimum of the topological entropies of all the symbolic extensions. This answers positively a conjecture of S.Newhouse and T.Downarowicz in dimension two and improves a previous result of the author \cite{burinv}.

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在表面上的中间平滑的符号扩展

我们证明了紧曲面上$\mathcal{C}^r$与$r>1$的映射具有符号扩展，即拓扑扩展是有限字母上的子位移。更准确地说，我们给出了所谓的符号扩展熵的一个明显的上界，它是所有符号扩展的拓扑熵的最小值。这肯定地回答了S.Newhouse和T.Downarowicz在二维上的一个猜想，并改进了作者先前的一个结果\cite{burinv}。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annales Scientifiques De L Ecole Normale Superieure 数学-数学

CiteScore

3.00

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics. Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition. The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.