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Type: Artigo de periódico
Title: A Multiplicative Ergodic Theorem For Rotation Numbers
Author: Arnold L.
Martin L.S.
Abstract: Given a vector field X on a Riemannian manifold M of dimension at least 2 whose flow leaves a probability measure μ invariant, the multiplicative ergodic theorem tells us that μ-a.s. every tangent vector possesses a Lyapunov exponent (exponential growth rate) that is equal to one of finitely many basic exponents corresponding to X and μ. We prove that, in the case of a simple Lyapunov spectrum, every tangent plane μ-a.s. possesses a rotation number that is equal to one of finitely many basic rotation numbers corresponding to X and μ. Rotation in a plane is measured as the time average of the infinitesimal changes of the angle between a frame moved by the linearized flow and the same frame parallel-transported by a (canonical) connection. © 1989 Plenum Publishing Corporation.
Editor: Kluwer Academic Publishers-Plenum Publishers
Rights: fechado
Identifier DOI: 10.1007/BF01048792
Date Issue: 1989
Appears in Collections:Unicamp - Artigos e Outros Documentos

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