On Local Constancy of Topological Entropy for Certain Partially Hyperbolic Diffeomorphisms

Let f : M → M be a partially hyperbolic diffeomorphism on a closed Riemannian manifold with uniformly compact center foliation. We show that if the center foliation of f is of dimension one then the topological entropy is constant on a small C 1 neighborhood of f .

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Bibliographic Details
Published inActa Mathematicae Applicatae Sinica Vol. 34; no. 2; pp. 249 - 253
Main Authors Wang, Lin, Wang, Xin-sheng, Zhu, Yu-jun
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2018
Springer Nature B.V
EditionEnglish series
Subjects
Applications of Mathematics
Entropy
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Riemann manifold
Theoretical
topological entropy
37B40
partially hyperbolic diffeomorphism
local constancy
37D30
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Summary:Let f : M → M be a partially hyperbolic diffeomorphism on a closed Riemannian manifold with uniformly compact center foliation. We show that if the center foliation of f is of dimension one then the topological entropy is constant on a small C 1 neighborhood of f .
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-018-0754-x