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On simultaneous linearization of diffeomorphisms of the sphere

2007; Duke University Press; Volume: 136; Issue: 3 Linguagem: Inglês

10.1215/s0012-7094-07-13633-0

1547-7398

Dmitry Dolgopyat, Raphaël Krikorian,

Quantum chaos and dynamical systems

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