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Local rigidity of Lyapunov spectrum for toral automorphisms
Israel Journal of Mathematics ( IF 0.8 ) Pub Date : 2020-06-05 , DOI: 10.1007/s11856-020-2028-6
Andrey Gogolev , Boris Kalinin , Victoria Sadovskaya

We study the regularity of the conjugacy between an Anosov automorphism L of a torus and its small perturbation. We assume that L has no more than two eigenvalues of the same modulus and that L 4 is irreducible over ℚ. We consider a volume-preserving C 1 -small perturbation f of L . We show that if Lyapunov exponents of f with respect to the volume are the same as Lyapunov exponents of L , then f is C 1+Hölder conjugate to L . Further, we establish a similar result for irreducible partially hyperbolic automorphisms with two-dimensional center bundle.

中文翻译:

环自同构的李雅普诺夫谱的局部刚性

我们研究了环面的 Anosov 自同构 L 与其小扰动之间的共轭规律。我们假设 L 具有不超过两个相同模数的特征值,并且 L 4 在 ℚ 上是不可约的。我们考虑 L 的体积保持 C 1 -小扰动 f。我们证明,如果 f 相对于体积的李雅普诺夫指数与 L 的李雅普诺夫指数相同,则 f 是 C 1+Hölder 与 L 的共轭。此外,我们为具有二维中心丛的不可约部分双曲自同构建立了类似的结果。
更新日期:2020-06-05
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