TY - JOUR
T1 - Lyapunov exponents and rigidity of Anosov automorphisms and skew products
AU - SAGHIN, RADU
AU - Yang, Jiagang
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/10/15
Y1 - 2019/10/15
N2 - In this paper we obtain local rigidity results for linear Anosov diffeomorphisms in terms of Lyapunov exponents. More specifically, we show that given an irreducible linear hyperbolic automorphism L with simple real eigenvalues with distinct absolute values, any small perturbation preserving the volume and with the same Lyapunov exponents is smoothly conjugate to L. We also obtain rigidity results for skew products over Anosov diffeomorphisms. Given a volume preserving partially hyperbolic skew product diffeomorphism f0 over an Anosov automorphism of the 2-torus, we show that for any volume preserving perturbation f of f0 with the same average stable and unstable Lyapunov exponents, the center foliation is smooth.
AB - In this paper we obtain local rigidity results for linear Anosov diffeomorphisms in terms of Lyapunov exponents. More specifically, we show that given an irreducible linear hyperbolic automorphism L with simple real eigenvalues with distinct absolute values, any small perturbation preserving the volume and with the same Lyapunov exponents is smoothly conjugate to L. We also obtain rigidity results for skew products over Anosov diffeomorphisms. Given a volume preserving partially hyperbolic skew product diffeomorphism f0 over an Anosov automorphism of the 2-torus, we show that for any volume preserving perturbation f of f0 with the same average stable and unstable Lyapunov exponents, the center foliation is smooth.
KW - Anosov diffeomorphism
KW - Lyapunov exponents
KW - Partially hyperbolic diffeomorphism
KW - Rigidity
UR - http://www.scopus.com/inward/record.url?scp=85070903956&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2019.106764
DO - 10.1016/j.aim.2019.106764
M3 - Article
AN - SCOPUS:85070903956
VL - 355
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
M1 - 106764
ER -