Local rigidity of certain actions of solvable groups on the boundaries of rank-one symmetric spaces
Dynamics of 2-interval piecewise affine maps and Hecke-Mahler series
2021, 17: 65-109. doi: 10.3934/jmd.2021003
Local Lyapunov spectrum rigidity of nilmanifold automorphisms
Jonathan DeWitt
Department of Mathematics, University of Chicago, 5734 South University Avenue, Chicago, IL 60637, USA
Received January 22, 2020 Revised November 04, 2020 Published February 2021
Fund Project: This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1746045
We study the regularity of a conjugacy between an Anosov automorphism $ L $ of a nilmanifold $ N/\Gamma $ and a volume-preserving, $ C^1 $-small perturbation $ f $. We say that $ L $ is locally Lyapunov spectrum rigid if this conjugacy is $ C^{1+} $ whenever $ f $ is $ C^{1+} $ and has the same volume Lyapunov spectrum as $ L $. For $ L $ with simple spectrum, we show that local Lyapunov spectrum rigidity is equivalent to $ L $ satisfying both an irreducibility condition and an ordering condition on its Lyapunov exponents.
Keywords: Lyapunov exponents, rigidity, nilmanifolds, coarse geometry.
Mathematics Subject Classification: Primary:37D20, 37D25;Secondary:51F30.
Citation: Jonathan DeWitt. Local Lyapunov spectrum rigidity of nilmanifold automorphisms. Journal of Modern Dynamics, 2021, 17: 65-109. doi: 10.3934/jmd.2021003
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