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A generic bounded linear cocycle has simple Lyapunov spectrum


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.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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