TY - JOUR
T1 - SMOOTH LOCAL RIGIDITY FOR HYPERBOLIC TORAL AUTOMORPHISMS
AU - Kalinin, Boris
AU - Sadovskaya, Victoria
AU - Wang, Zhenqi Jenny
N1 - Publisher Copyright:
© 2023 by the author(s) under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License (CC BY NC ND 4.0). (CC BY NC 3.0)
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/inward/citedby.url?scp=105002993142&partnerID=8YFLogxK
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 -