Simplicity of Lyapunov spectrum for linear cocycles over non-uniformly hyperbolic systems
We prove that generic fiber-bunched and Hölder continuous linear cocycles over a non-uniformly hyperbolic system endowed with a $u$-Gibbs measure have simple Lyapunov spectrum. This gives an affirmative answer to a conjecture proposed by Viana in the context of fiber-bunched linear cocycles.
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| Published in | Ergodic theory and dynamical systems Vol. 40; no. 11; pp. 2947 - 2969 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.11.2020
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0143-3857 1469-4417 |
| DOI | 10.1017/etds.2019.22 |
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| Abstract | We prove that generic fiber-bunched and Hölder continuous linear cocycles over a non-uniformly hyperbolic system endowed with a $u$-Gibbs measure have simple Lyapunov spectrum. This gives an affirmative answer to a conjecture proposed by Viana in the context of fiber-bunched linear cocycles. |
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| AbstractList | We prove that generic fiber-bunched and Hölder continuous linear cocycles over a non-uniformly hyperbolic system endowed with a
$u$
-Gibbs measure have simple Lyapunov spectrum. This gives an affirmative answer to a conjecture proposed by Viana in the context of fiber-bunched linear cocycles. We prove that generic fiber-bunched and Hölder continuous linear cocycles over a non-uniformly hyperbolic system endowed with a \(u\)-Gibbs measure have simple Lyapunov spectrum. This gives an affirmative answer to a conjecture proposed by Viana in the context of fiber-bunched linear cocycles. |
| Author | LIMA, YURI BACKES, LUCAS POLETTI, MAURICIO VARANDAS, PAULO |
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| Keywords | 37H15 linear cocyles 37D25 Lyapunov exponents non-uniform hyperbolicity 37D30 |
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| Snippet | We prove that generic fiber-bunched and Hölder continuous linear cocycles over a non-uniformly hyperbolic system endowed with a $u$-Gibbs measure have simple... We prove that generic fiber-bunched and Hölder continuous linear cocycles over a non-uniformly hyperbolic system endowed with a $u$ -Gibbs measure have simple... We prove that generic fiber-bunched and Hölder continuous linear cocycles over a non-uniformly hyperbolic system endowed with a \(u\)-Gibbs measure have simple... |
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| Title | Simplicity of Lyapunov spectrum for linear cocycles over non-uniformly hyperbolic systems |
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