Dominated Splitting from Constant Periodic Data and Global Rigidity of Anosov Automorphisms

We show that a cocycle over a hyperbolic system with constant periodic data has a dominated splitting whenever the periodic data indicates it should. This implies global periodic data rigidity of generic Anosov automorphisms of . Further, our approach also works when the periodic data is narrow, tha...

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Published inGeometric and functional analysis Vol. 34; no. 5; pp. 1370 - 1398
Main Authors DeWitt, Jonathan, Gogolev, Andrey
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2024
Springer Nature B.V
Subjects
Analysis
Automorphisms
Hyperbolic systems
Isomorphism
Mathematics
Mathematics and Statistics
Rigidity
Splitting
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Summary:We show that a cocycle over a hyperbolic system with constant periodic data has a dominated splitting whenever the periodic data indicates it should. This implies global periodic data rigidity of generic Anosov automorphisms of . Further, our approach also works when the periodic data is narrow, that is, sufficiently close to constant. We can show global periodic data rigidity for certain non-linear Anosov diffeomorphisms in a neighborhood of an irreducible Anosov automorphism with simple spectrum.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-024-00680-z