Global rigidity of smooth \mathbb Z\ltimes_λ\mathbb R-actions on \mathbb T²

2024/03/15 by Changguang Dong, Yi Shi, Dong, Changguang +1
Mathematics · #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2403.10060

Abstract

For λ>1, we consider the locally free \mathbb Z\ltimes_λ\mathbb R actions on \mathbb T². We show that, if the action is C^r with r≥2, then it is C^r-ε-conjugate to an affine action generated by a hyperbolic automorphism and a linear translation flow along expanding eigen-direction of the automorphism. In contrast, there exists a C^1+α-action which is semi-conjugate, but not topologically conjugate to an affine action.

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