TY - JOUR
T1 - Local rigidity for Anosov automorphisms
AU - Gogolev, Andrey
AU - Kalinin, Boris
AU - Sadovskaya, Victoria
AU - De La Llave, Rafael
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
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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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 -