Topological entropy on subsets for fixed-point free flows

Dou Dou; Meng Fan; Hua Qiu

doi:10.3934/dcds.2017273

Article Contents

2017, Volume 37, Issue 12: 6319-6331. Doi: 10.3934/dcds.2017273

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Topological entropy on subsets for fixed-point free flows

Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, China

* Corresponding author
* Corresponding author

Received: December 31, 2016

Revised: June 30, 2017

Published: October 2017

The first author was supported by the National Nature Science Foundation of China (Grant No. 10901080,11271191 and 11431012) and CSC. The third author was supported by the National Nature Science Foundation of China (Grant No. 11471157).

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Abstract

By considering all possible reparametrizations of the flows instead of the time- $1$ maps, we introduce Bowen topological entropy and local entropy on subsets for flows. Through handling techniques for reparametrization balls, we prove a covering lemma for fixed-point free flows and then prove a variational principle.

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Mathematics Subject Classification: Primary: 37B40, 54H20.

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References

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