Density of positive Lyapunov exponents for symplectic cocycles

Abstract

We prove that Sp(2d;R), HSp(2d) and pseudo unitary cocycles with at least one non-zero Lyapunov exponent are dense in all usual regularity classes for non periodic dynamical systems. For Schrödinger operators on the strip, we prove a similar result for density of positive Lyapunov exponents.

References in corpus (4)

• Efficient computation of the Zassenhaus formula
• Complex one-frequency cocycles
• Positive Lyapunov exponents for higher dimensional quasiperiodic cocycles
• Density of positive Lyapunov exponents for SL(2,R) cocycles

Cited by in corpus (3)

• Positivity of the top Lyapunov exponent for cocycles on semisimple Lie groups over hyperbolic bases
• Rotation numbers of perturbations of smooth dynamics
• Positive Lyapunov exponents for cocycles over time one anosov maps