On simultaneous linearization of diffeomorphisms of the sphere

Abstract

Let R1,R2,…,Rm be rotations generating SOd+1, d≥2, and let f1,f2,…,fm be small smooth perturbations of them. We show that {fα} 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