Simultaneous Linearization of Diffeomorphisms of Isotropic Manifolds

arXiv2009.08599MaRDI QIDQ6349360

Publication date: 17 September 2020

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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