Positivity of the Top Lyapunov Exponent for Cocycles on Semisimple Lie Groups over Hyperbolic Bases

Mário Bessa; Jairo Bochi; Michel Cambrainha; Carlos Matheus; Paulo Varandas; Disheng Xu

doi:10.1007/s00574-017-0048-6

Positivity of the Top Lyapunov Exponent for Cocycles on Semisimple Lie Groups over Hyperbolic Bases

Mário Bessa, Jairo Bochi, Michel Cambrainha, Carlos Matheus, Paulo Varandas, Disheng Xu

Mathematics

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

4 Scopus citations

Abstract

A theorem of Viana says that almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents. In this note we extend this result to cocycles on any noncompact classical semisimple Lie group.

Original language	English (US)
Pages (from-to)	73-87
Number of pages	15
Journal	Bulletin of the Brazilian Mathematical Society
Volume	49
Issue number	1
DOIs	https://doi.org/10.1007/s00574-017-0048-6
State	Published - Mar 1 2018

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "Positivity of the Top Lyapunov Exponent for Cocycles on Semisimple Lie Groups over Hyperbolic Bases",

abstract = "A theorem of Viana says that almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents. In this note we extend this result to cocycles on any noncompact classical semisimple Lie group.",

author = "M{\'a}rio Bessa and Jairo Bochi and Michel Cambrainha and Carlos Matheus and Paulo Varandas and Disheng Xu",

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AU - Bessa, Mário

AU - Bochi, Jairo

AU - Cambrainha, Michel

AU - Matheus, Carlos

AU - Varandas, Paulo

AU - Xu, Disheng

PY - 2018/3/1

Y1 - 2018/3/1

N2 - A theorem of Viana says that almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents. In this note we extend this result to cocycles on any noncompact classical semisimple Lie group.

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Positivity of the Top Lyapunov Exponent for Cocycles on Semisimple Lie Groups over Hyperbolic Bases

Abstract

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