The entropy conjecture for diffeomorphisms away from tangencies

Liao, Gang
Viana, Marcelo
Yang, Jiagang

Open link

Publication date

January 2013

DOI

10.4171/JEMS/413

Publisher

journal of the european mathematical society

ISSN

1435-9855

Journal

issn:1435-9855

Abstract

We prove that every C-1 diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant. Consequently, such diffeomorphisms satisfy Shub's entropy conjecture: the entropy is bounded from below by the spectral radius in homology. Moreover, they admit principal symbolic extensions, and the topological entropy and metrical entropy vary upper semicontinuously with the map. In contrast, generic diffeomorphisms with persistent tangencies are not entropy expansive.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000326323400003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Mathematics, AppliedMa...