Entropy of partially hyperbolic flows with center dimension two

Mario Roldán, RADU SAGHIN, Jiagang Yang

Research output: Contribution to journalArticlepeer-review

Abstract

In this article we study the regularity of the topological and metric entropy of partially hyperbolic flows with two-dimensional center direction. We show that the topological entropy is upper semicontinuous with respect to the flow, and we give an example where the lower semicontinuity fails. We also show that if such a flow has no fixed points, then it is entropy expansive, and consequentely the metric entropy function is upper semicontinuous, there exist equilibrium states (and measures of maximal entropy), and principal symbolic extensions.

Original languageEnglish
Pages (from-to)790-806
Number of pages17
JournalNonlinearity
Volume33
Issue number2
DOIs
StatePublished - 2020
Externally publishedYes

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