Positive Lyapunov exponents for higher dimensional quasiperiodic cocycles

Abstract

We consider an m-dimensional analytic cocycle with underlying dynamics given by an irrational translation on the circle. Assuming that the d-dimensional upper left corner of the cocycle is typically large enough, we prove that the d largest Lyapunov exponents associated with this cocycle are bounded away from zero. The result is uniform relative to certain measurements on the matrix blocks forming the cocycle. As an application of this result, we obtain nonperturbative (in the spirit of Sorets-Spencer theorem) positive lower bounds of the nonnegative Lyapunov exponents for various models of band lattice Schroedinger operators.

37 pages

References in corpus (1)

• Regularity and convergence rates for the Lyapunov exponents of linear co-cycles

Cited by in corpus (8)

• Dynamics and spectral theory of quasi-periodic Schrödinger-type operators
• Continuity of the Lyapunov exponents for quasiperiodic cocycles
• Dominated splittings and the spectrum of singular quasi-periodic Jacobi operators
• Density of positive Lyapunov exponents for symplectic cocycles
• Subcritical behavior for quasi-periodic Schrödinger cocycles with trigonometric potentials
• Positivity of the top Lyapunov exponent for cocycles on semisimple Lie groups over hyperbolic bases
• Singular analytic linear cocycles with negative infinite Lyapunov exponents
• Large coupling asymptotics for the Lyapunov exponent of quasi-periodic Schrödinger operators with analytic potentials