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

Universidade da Beira Interior
Facultad de Matemáticas
Universidade Federal do Estado do Rio de Janeiro
University Paris 13
Federal University of Bahia
Paris Descartes University

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

5 Citations (Scopus)

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
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
Publication status	Published - 1 Mar 2018
Externally published	Yes

Keywords

Linear cocycles
Lyapunov exponents
Semisimple Lie groups

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10.1007/s00574-017-0048-6

Cite this

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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.",

keywords = "Linear cocycles, Lyapunov exponents, Semisimple Lie groups",

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

note = "Publisher Copyright: {\textcopyright} 2017, Sociedade Brasileira de Matem{\'a}tica.",

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T1 - Positivity of the Top Lyapunov Exponent for Cocycles on Semisimple Lie Groups over Hyperbolic Bases

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.

AB - 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.

KW - Linear cocycles

KW - Lyapunov exponents

KW - Semisimple Lie groups

U2 - 10.1007/s00574-017-0048-6

DO - 10.1007/s00574-017-0048-6

M3 - Article

AN - SCOPUS:85021814216

SN - 1678-7544

VL - 49

SP - 73

EP - 87

JO - Bulletin of the Brazilian Mathematical Society

JF - Bulletin of the Brazilian Mathematical Society

IS - 1

ER -

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

Abstract

Keywords

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