Stable ergodicity of skew products

Keith Burns; Amie Wilkinson

doi:10.1016/S0012-9593(00)87721-6

Stable ergodicity of skew products

Keith Burns^*, Amie Wilkinson

^*Corresponding author for this work

Mathematics

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

42 Scopus citations

Abstract

Stable ergodicity is dense among compact Lie group extensions of Anosov diffeomorphisms of compact manifolds. Under the additional assumption that the base map acts on an infranilmanifold, an extension that is not stably ergodic must have a factor that has one of three special forms. A consequence is that stable ergodicity and stable ergodicity within skew products are equivalent in this case.

Original language	English (US)
Pages (from-to)	859-889
Number of pages	31
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	32
Issue number	6
DOIs	https://doi.org/10.1016/S0012-9593(00)87721-6
State	Published - 1999

Funding

A detailed formulation of the above results will be found in Se’ction 4. We would like to thank Mike Field, John Franks and Charles Pugh for several helpful discussions and Viorel Nificg for introducing us to Brin’s papers. The first author was partially supported by NSF Grant DMS 9504760.

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1016/S0012-9593(00)87721-6

Cite this

@article{b9ab5751abfa4cc7ac6378fa92ce2bd1,

title = "Stable ergodicity of skew products",

abstract = "Stable ergodicity is dense among compact Lie group extensions of Anosov diffeomorphisms of compact manifolds. Under the additional assumption that the base map acts on an infranilmanifold, an extension that is not stably ergodic must have a factor that has one of three special forms. A consequence is that stable ergodicity and stable ergodicity within skew products are equivalent in this case.",

author = "Keith Burns and Amie Wilkinson",

note = "Funding Information: A detailed formulation of the above results will be found in Se{\textquoteright}ction 4. We would like to thank Mike Field, John Franks and Charles Pugh for several helpful discussions and Viorel Nificg for introducing us to Brin{\textquoteright}s papers. The first author was partially supported by NSF Grant DMS 9504760.",

year = "1999",

doi = "10.1016/S0012-9593(00)87721-6",

language = "English (US)",

volume = "32",

pages = "859--889",

journal = "Annales Scientifiques de l'Ecole Normale Superieure",

issn = "0012-9593",

publisher = "Societe Mathematique de France",

number = "6",

}

TY - JOUR

T1 - Stable ergodicity of skew products

AU - Burns, Keith

AU - Wilkinson, Amie

N1 - Funding Information: A detailed formulation of the above results will be found in Se’ction 4. We would like to thank Mike Field, John Franks and Charles Pugh for several helpful discussions and Viorel Nificg for introducing us to Brin’s papers. The first author was partially supported by NSF Grant DMS 9504760.

PY - 1999

Y1 - 1999

N2 - Stable ergodicity is dense among compact Lie group extensions of Anosov diffeomorphisms of compact manifolds. Under the additional assumption that the base map acts on an infranilmanifold, an extension that is not stably ergodic must have a factor that has one of three special forms. A consequence is that stable ergodicity and stable ergodicity within skew products are equivalent in this case.

AB - Stable ergodicity is dense among compact Lie group extensions of Anosov diffeomorphisms of compact manifolds. Under the additional assumption that the base map acts on an infranilmanifold, an extension that is not stably ergodic must have a factor that has one of three special forms. A consequence is that stable ergodicity and stable ergodicity within skew products are equivalent in this case.

UR - http://www.scopus.com/inward/record.url?scp=0033472563&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033472563&partnerID=8YFLogxK

U2 - 10.1016/S0012-9593(00)87721-6

DO - 10.1016/S0012-9593(00)87721-6

M3 - Article

AN - SCOPUS:0033472563

SN - 0012-9593

VL - 32

SP - 859

EP - 889

JO - Annales Scientifiques de l'Ecole Normale Superieure

JF - Annales Scientifiques de l'Ecole Normale Superieure

IS - 6

ER -

Stable ergodicity of skew products

Abstract

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this