SMOOTH LOCAL RIGIDITY FOR HYPERBOLIC TORAL AUTOMORPHISMS

Boris Kalinin; Victoria Sadovskaya; Zhenqi Jenny Wang

doi:10.1090/cams/22

SMOOTH LOCAL RIGIDITY FOR HYPERBOLIC TORAL AUTOMORPHISMS

Boris Kalinin
, Victoria Sadovskaya
, Zhenqi Jenny Wang

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

5 Scopus citations

Abstract

We study the regularity of a conjugacy H between a hyperbolic toral automorphism A and its smooth perturbation f. We show that if H is weakly differentiable then it is C^1+Hölder and, if A is also weakly irreducible, then H is C^∞. As a part of the proof, we establish results of independent interest on Hölder continuity of a measurable conjugacy between linear cocycles over a hyperbolic system. As a corollary, we improve regularity of the conjugacy to C∞ in prior local rigidity results.

Original language	English (US)
Pages (from-to)	290-328
Number of pages	39
Journal	Communications of the American Mathematical Society
Volume	3
DOIs	https://doi.org/10.1090/cams/22
State	Published - 2023

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)
Applied Mathematics

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title = "SMOOTH LOCAL RIGIDITY FOR HYPERBOLIC TORAL AUTOMORPHISMS",

abstract = "We study the regularity of a conjugacy H between a hyperbolic toral automorphism A and its smooth perturbation f. We show that if H is weakly differentiable then it is C1+H{\"o}lder and, if A is also weakly irreducible, then H is C∞. As a part of the proof, we establish results of independent interest on H{\"o}lder continuity of a measurable conjugacy between linear cocycles over a hyperbolic system. As a corollary, we improve regularity of the conjugacy to C∞ in prior local rigidity results.",

author = "Boris Kalinin and Victoria Sadovskaya and Wang, \{Zhenqi Jenny\}",

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doi = "10.1090/cams/22",

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T1 - SMOOTH LOCAL RIGIDITY FOR HYPERBOLIC TORAL AUTOMORPHISMS

AU - Kalinin, Boris

AU - Sadovskaya, Victoria

AU - Wang, Zhenqi Jenny

PY - 2023

Y1 - 2023

N2 - We study the regularity of a conjugacy H between a hyperbolic toral automorphism A and its smooth perturbation f. We show that if H is weakly differentiable then it is C1+Hölder and, if A is also weakly irreducible, then H is C∞. As a part of the proof, we establish results of independent interest on Hölder continuity of a measurable conjugacy between linear cocycles over a hyperbolic system. As a corollary, we improve regularity of the conjugacy to C∞ in prior local rigidity results.

AB - We study the regularity of a conjugacy H between a hyperbolic toral automorphism A and its smooth perturbation f. We show that if H is weakly differentiable then it is C1+Hölder and, if A is also weakly irreducible, then H is C∞. As a part of the proof, we establish results of independent interest on Hölder continuity of a measurable conjugacy between linear cocycles over a hyperbolic system. As a corollary, we improve regularity of the conjugacy to C∞ in prior local rigidity results.

UR - https://www.scopus.com/pages/publications/105002993142

UR - https://www.scopus.com/pages/publications/105002993142#tab=citedBy

U2 - 10.1090/cams/22

DO - 10.1090/cams/22

M3 - Article

AN - SCOPUS:105002993142

SN - 2692-3688

VL - 3

SP - 290

EP - 328

JO - Communications of the American Mathematical Society

JF - Communications of the American Mathematical Society

ER -

SMOOTH LOCAL RIGIDITY FOR HYPERBOLIC TORAL AUTOMORPHISMS

Abstract

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