A generic bounded linear cocycle has simple Lyapunov spectrum

DOI10.1017/S0143385705000337zbMath1130.37312MaRDI QIDQ5717907

Nguyen Dinh Cong

Publication date: 13 January 2006

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Mathematics Subject Classification ID

Stability of topological dynamical systems (37B25) Partially hyperbolic systems and dominated splittings (37D30) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) Topological dynamics of nonautonomous systems (37B55)

Related Items (11)

On analyticity for Lyapunov exponents of generic bounded linear random dynamical systems ⋮ On integral separation of bounded linear random differential equations ⋮ Dynamics of generic 2-dimensional linear differential systems ⋮ On the Lyapunov exponent of certain \(SL (2,\mathbb R)\)-valued cocycles. II ⋮ Lyapunov exponents for linear homogeneous differential equations ⋮ Fine properties of \(L^p\)-cocycles which allow abundance of simple and trivial spectrum ⋮ A uniform dichotomy for generic ${\rm SL}(2,{\mathbb{R}})$ cocycles over a minimal base ⋮ Hyperbolicity and integral expression of the Lyapunov exponents for linear cocycles ⋮ Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts ⋮ Trivial and simple spectrum for \(\mathrm{SL}(d, \mathbb{R})\) cocycles with free base and fiber dynamics ⋮ Remarks on linear-quadratic dissipative control systems

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