Simultaneous Linearization of Diffeomorphisms of Isotropic Manifolds

Jonathan DeWitt

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arXiv · 2009.08599

Simultaneous Linearization of Diffeomorphisms of Isotropic Manifolds

Jonathan DeWitt

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Abstract

Suppose that $M$ is a closed isotropic Riemannian manifold and that $R_1,...,R_m$ generate the isometry group of $M$. Let $f_1,...,f_m$ be smooth perturbations of these isometries. We show that the $f_i$ are simultaneously conjugate to isometries if and only if their associated uniform Bernoulli random walk has all Lyapunov exponents zero. This extends a linearization result of Dolgopyat and Krikorian from $S^n$ to real, complex, and quaternionic projective spaces. In addition, we identify and remedy an oversight in that earlier work.

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Jonathan DeWitt. 2020-09-18. Simultaneous Linearization of Diffeomorphisms of Isotropic Manifolds. https://arxiv.org/abs/2009.08599

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