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A generic bounded linear cocycle has simple Lyapunov spectrum

Published online by Cambridge University Press:  07 October 2005

NGUYEN DINH CONG
NGUYEN DINH CONG
Affiliation:
Hanoi Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam (e-mail: [email protected])
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Abstract

We show that the set of cocycles with integral separateness is open and dense in the space of all bounded $Gl(d,{\mathbb R})$-cocycles equipped with uniform topology. As a consequence, a generic bounded linear cocycle has simple Lyapunov spectrum and dominated Oseledets splitting, and a generic bounded $Sl(2,\mathbb R)$-cocycle is uniformly hyperbolic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 6 , December 2005 , pp. 1775 - 1797
Copyright
2005 Cambridge University Press

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