Local rigidity for Anosov automorphisms

Andrey Gogolev; Boris Kalinin; Victoria Sadovskaya; Rafael De La Llave

doi:10.4310/MRL.2011.v18.n5.a4

Local rigidity for Anosov automorphisms

Andrey Gogolev
, Boris Kalinin
, Victoria Sadovskaya
, Rafael De La Llave

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

22 Scopus citations

Abstract

We consider an irreducible Anosov automorphism L of a torus T^d such that no three eigenvalues have the same modulus. We show that L is locally rigid, that is, L is C^1+Hölder1 conjugate to any C ¹-small perturbation f such that the derivative Dpfn is conjugate to Ln whenever fnp = p. We also prove that toral automorphisms satisfying these assumptions are generic in SL(d, ℤ). Examples constructed in the Appendix show the importance of the assumption on the eigenvalues.

Original language	English (US)
Pages (from-to)	843-858
Number of pages	16
Journal	Mathematical Research Letters
Volume	18
Issue number	5
DOIs	https://doi.org/10.4310/MRL.2011.v18.n5.a4
State	Published - Sep 2011

All Science Journal Classification (ASJC) codes

General Mathematics

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10.4310/MRL.2011.v18.n5.a4

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title = "Local rigidity for Anosov automorphisms",

abstract = "We consider an irreducible Anosov automorphism L of a torus Td such that no three eigenvalues have the same modulus. We show that L is locally rigid, that is, L is C1+H{\"o}lder1 conjugate to any C 1-small perturbation f such that the derivative Dpfn is conjugate to Ln whenever fnp = p. We also prove that toral automorphisms satisfying these assumptions are generic in SL(d, ℤ). Examples constructed in the Appendix show the importance of the assumption on the eigenvalues.",

author = "Andrey Gogolev and Boris Kalinin and Victoria Sadovskaya and \{De La Llave\}, Rafael",

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T1 - Local rigidity for Anosov automorphisms

AU - Gogolev, Andrey

AU - Kalinin, Boris

AU - Sadovskaya, Victoria

AU - De La Llave, Rafael

PY - 2011/9

Y1 - 2011/9

N2 - We consider an irreducible Anosov automorphism L of a torus Td such that no three eigenvalues have the same modulus. We show that L is locally rigid, that is, L is C1+Hölder1 conjugate to any C 1-small perturbation f such that the derivative Dpfn is conjugate to Ln whenever fnp = p. We also prove that toral automorphisms satisfying these assumptions are generic in SL(d, ℤ). Examples constructed in the Appendix show the importance of the assumption on the eigenvalues.

AB - We consider an irreducible Anosov automorphism L of a torus Td such that no three eigenvalues have the same modulus. We show that L is locally rigid, that is, L is C1+Hölder1 conjugate to any C 1-small perturbation f such that the derivative Dpfn is conjugate to Ln whenever fnp = p. We also prove that toral automorphisms satisfying these assumptions are generic in SL(d, ℤ). Examples constructed in the Appendix show the importance of the assumption on the eigenvalues.

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UR - https://www.scopus.com/pages/publications/84856101642#tab=citedBy

U2 - 10.4310/MRL.2011.v18.n5.a4

DO - 10.4310/MRL.2011.v18.n5.a4

M3 - Article

AN - SCOPUS:84856101642

SN - 1073-2780

VL - 18

SP - 843

EP - 858

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 5

ER -

Local rigidity for Anosov automorphisms

Abstract

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