Perturbations with nonpositive Lyapunov exponents

Abstract

The notion of uniform hyperbolicity is equivalent to various admissibility properties. For example, one such property is expressed in terms of the existence of bounded solutions for any bounded perturbation of the dynamics. Our main objective is to describe a weaker hyperbolicity property for a nonautonomous dynamics with discrete time that is equivalent to a modification of the latter admissibility property, namely the existence of solutions with nonpositive Lyapunov exponents for any perturbation with nonpositive Lyapunov exponent. Our characterization is expressed in terms of appropriate exponents that somehow mix the Bohl exponents and the Lyapunov exponents.