Invariance of entropy for maps isotopic to Anosov

Pablo D. Carrasco; Cristina Lizana; Enrique Pujals; Carlos H. Vásquez

doi:10.1088/1361-6544/abdfb3

Invariance of entropy for maps isotopic to Anosov

Pablo D. Carrasco, Cristina Lizana, Enrique Pujals, Carlos H. Vásquez

INSTITUTE OF MATHEMATICS

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We prove the topological entropy remains constant inside the class of partially hyperbolic diffeomorphisms of Td with simple central bundle (that is, when it decomposes into one dimensional sub-bundles with controlled geometry) and such that their induced action on H1 (Td) is hyperbolic. In absence of the simplicity condition we construct a robustly transitive counter-example.

Original language	English
Pages (from-to)	1612-1632
Number of pages	21
Journal	Nonlinearity
Volume	34
Issue number	3
DOIs	https://doi.org/10.1088/1361-6544/abdfb3
State	Published - Mar 2021

Keywords

derived from Anosov
measures of maximal entropy
partial hyperbolicity
robustly transitive diffeomorphisms

Access to Document

10.1088/1361-6544/abdfb3

Cite this

@article{2970d95b6c2941c8b77c0ba12d49a233,

title = "Invariance of entropy for maps isotopic to Anosov",

abstract = "We prove the topological entropy remains constant inside the class of partially hyperbolic diffeomorphisms of Td with simple central bundle (that is, when it decomposes into one dimensional sub-bundles with controlled geometry) and such that their induced action on H1 (Td) is hyperbolic. In absence of the simplicity condition we construct a robustly transitive counter-example.",

keywords = "derived from Anosov, measures of maximal entropy, partial hyperbolicity, robustly transitive diffeomorphisms",

author = "Carrasco, {Pablo D.} and Cristina Lizana and Enrique Pujals and V{\'a}squez, {Carlos H.}",

note = "Publisher Copyright: {\textcopyright} 2021 IOP Publishing Ltd & London Mathematical Society.",

year = "2021",

month = mar,

doi = "10.1088/1361-6544/abdfb3",

language = "English",

volume = "34",

pages = "1612--1632",

journal = "Nonlinearity",

issn = "0951-7715",

publisher = "IOP Publishing Ltd.",

number = "3",

}

TY - JOUR

T1 - Invariance of entropy for maps isotopic to Anosov

AU - Carrasco, Pablo D.

AU - Lizana, Cristina

AU - Pujals, Enrique

AU - Vásquez, Carlos H.

PY - 2021/3

Y1 - 2021/3

N2 - We prove the topological entropy remains constant inside the class of partially hyperbolic diffeomorphisms of Td with simple central bundle (that is, when it decomposes into one dimensional sub-bundles with controlled geometry) and such that their induced action on H1 (Td) is hyperbolic. In absence of the simplicity condition we construct a robustly transitive counter-example.

AB - We prove the topological entropy remains constant inside the class of partially hyperbolic diffeomorphisms of Td with simple central bundle (that is, when it decomposes into one dimensional sub-bundles with controlled geometry) and such that their induced action on H1 (Td) is hyperbolic. In absence of the simplicity condition we construct a robustly transitive counter-example.

KW - derived from Anosov

KW - measures of maximal entropy

KW - partial hyperbolicity

KW - robustly transitive diffeomorphisms

UR - http://www.scopus.com/inward/record.url?scp=85103374230&partnerID=8YFLogxK

U2 - 10.1088/1361-6544/abdfb3

DO - 10.1088/1361-6544/abdfb3

M3 - Article

AN - SCOPUS:85103374230

SN - 0951-7715

VL - 34

SP - 1612

EP - 1632

JO - Nonlinearity

JF - Nonlinearity

IS - 3

ER -

Invariance of entropy for maps isotopic to Anosov

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this