2018/08/19 by Andrey Gogolev, Boris Kalinin, Gogolev, Andrey +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS
paper · pdf · doi:10.48550/arxiv.1808.06249
12 pages. arXiv admin note: text overlap with arXiv:1009.2994
arxiv created 2018/08/19 · arxiv updated 2018/08/22
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 L4 is irreducible over \mathbb Q. We consider a volume-preserving C1-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 C1+Hölder conjugate to L. Further, we establish a similar result for irreducible partially hyperbolic automorphisms with two-dimensional center bundle.