On simultaneous linearization of diffeomorphisms of the sphere

Dmitry Dolgopyat; Raphaël Krikorian

doi:10.1215/S0012-7094-07-13633-0

On simultaneous linearization of diffeomorphisms of the sphere

Dmitry Dolgopyat
, Raphaël Krikorian

Pennsylvania State University

Research output: Contribution to journal › Article › peer-review

Abstract

Let R₁, R₂, . . .,R_m be rotations generating double struk S sign double struk O sign_d+1, d ≥ 2, and let f₁, f₂, . . .,f_m be small smooth perturbations of them. We show that {f_α} 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.

Original language	English
Pages (from-to)	475-505
Number of pages	31
Journal	Duke Mathematical Journal
Volume	136
Issue number	3
DOIs	https://doi.org/10.1215/S0012-7094-07-13633-0
Publication status	Published - 15 Feb 2007

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title = "On simultaneous linearization of diffeomorphisms of the sphere",

abstract = "Let R1, R2, . . .,Rm be rotations generating double struk S sign double struk O signd+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.",

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N2 - Let R1, R2, . . .,Rm be rotations generating double struk S sign double struk O signd+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.

AB - Let R1, R2, . . .,Rm be rotations generating double struk S sign double struk O signd+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.

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JO - Duke Mathematical Journal

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On simultaneous linearization of diffeomorphisms of the sphere

Abstract

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