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Local Lyapunov Spectrum Rigidity of Nilmanifold Automorphisms

2019/11/18 by Jonathan DeWitt, DeWitt, Jonathan
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1911.07717

40 pages; comments are welcome

arxiv created 2019/11/18 · arxiv updated 2019/11/19

Abstract

We study the regularity of a conjugacy between an Anosov automorphism L of a nilmanifold N/Γ and a volume-preserving, C1-small perturbation f. We say that L is locally Lyapunov spectrum rigid if this conjugacy is C1+ whenever f is C1+ 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.

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