The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center
type: Item
instance of: scholarly article
title: The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center
zbMATH Open document ID: 1200.37027
author: Radu Saghin
author: Zhihong Xia
published in: Topology and its Applications
publication date: 2009-12-03T00:00:00Z
review text: Let \(M\) be a compact manifold and \(f: M\to M\) a diffeomorphism. Denote by \(f_{*,k}\) the corresponding automorphism of the \(k\)-th homology group. Then the spectral radius \(\mathrm{sp}(f_*)\) is defined to be the maximum of the spectral radii of the \(f_{*,k}\). Further, denote by \(h(f)\) the topological entropy of \(f\). The authors show that under specific hyperbolicity conditions on \(f\) the inequality \(h(f)\geq \mathrm{sp}(f_*)\) holds, thus proving a special case of Shub's conjecture of \textit{M. Shub} [Bull. Am. Math. Soc. 80, 27--41 (1974; Zbl 0305.58014)].
reviewed by: Joachim Hilgert
Mathematics Subject Classification ID: 37D30
zbMATH DE Number: 5641741
zbMATH Keywords: entropy conjecture
zbMATH Keywords: partially hyperbolic diffeomorphisms
zbMATH Keywords: spectral radius
zbMATH Keywords: topological entropy
MaRDI profile type: Publication
full work available at URL: j.topol.2009.04.053
OpenAlex ID: W2083847987
Wikidata QID: Q122879653
cites work: Q4171327
cites work: Handbook of dynamical systems. Volume 1A
cites work: Q3662280
cites work: Q4064701
cites work: Q4136188
cites work: Estimates of the topological entropy from below for continuous self-maps on some compact manifolds
cites work: Entropy and volume
cites work: Q4064750
cites work: Currents, flows and diffeomorphisms
cites work: Dynamical systems, filtrations and entropy
cites work: Entropy and stability
cites work: Volume growth and entropy
DOI: 10.1016/J.TOPOL.2009.04.053
description: scientific article; zbMATH DE number 5641741