Simultaneous linearization of diffeomorphisms of isotropic manifolds

  • Jonathan DeWitt

    University of Chicago, USA
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Abstract

Suppose that is a closed isotropic Riemannian manifold and that generate the isometry group of . Let be smooth perturbations of these isometries. We show that the 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 [Duke Math. J. {136}, 475–505 (2007)] from to real, complex, and quaternionic projective spaces. In addition, we identify and remedy an oversight in that earlier work.

Cite this article

Jonathan DeWitt, Simultaneous linearization of diffeomorphisms of isotropic manifolds. J. Eur. Math. Soc. 26 (2024), no. 8, pp. 2897–2969

DOI 10.4171/JEMS/1327