Lp-GENERIC COCYCLES HAVE ONE-POINT LYAPUNOV SPECTRUM-Reference-Cited by-同舟云学术

Lp-GENERIC COCYCLES HAVE ONE-POINT LYAPUNOV SPECTRUM

Published:2003-03 Issue:01 Volume:03 Page:73-81
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

Author:

ARBIETO ALEXANDER¹,BOCHI JAIRO¹

Affiliation:

1. IMPA, Estrada D. Castorina 110, Jardim Botânico, 22460-320 Rio de Janeiro, Brazil

Abstract

We show that the sum of the first k Lyapunov exponents of linear cocycles is an upper semicontinuous function in the Lp topologies, for any 1 ≤ p ≤ ∞ and k. This fact, together with a result from Arnold and Cong, implies that the Lyapunov exponents of the Lp-generic cocycle, p < ∞, are all equal.

Publisher

World Scientific Pub Co Pte Lt

Subject

Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219493703000619

Reference11 articles.

1. Random Dynamical Systems

2. On the simplicity of the Lyapunov spectrum of products of random matrices

3. Linear cocycles with simple Lyapunov spectrum are dense in $L^\infty$

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