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

We consider a C 1 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...

Full description

Saved in:
Bibliographic Details
Published inIsrael journal of mathematics Vol. 215; no. 2; pp. 857 - 875
Main Authors Saghin, Radu, Yang, Jiagang
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.09.2016
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Chaos theory
Continuity (mathematics)
Entropy
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Online AccessGet full text

Cover

More Information
Summary:We consider a C 1 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.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-016-1396-4