On simultaneous linearization of diffeomorphisms of the sphere

摘要

Let R-1, R-2,..., R-m, be rotations generating SOd+1, d >= 2, and let f(1), f(2),..., f(m) be small smooth perturbations of them. We show that {f(alpha)} can be linearized simultaneously if and only if the associated random walk has zero Lyapunov exponents. As a consequence, we obtain stable ergodicity of actions of random rotations in even dimensions.