TOPOLOGICAL CONJUGACY FOR LIPSCHITZ PERTURBATIONS OF NON-AUTONOMOUS SYSTEMS

Abstract

In this paper, topological conjugacy for two-sided non-hyperbolic and non-autonomous discrete dynamical systems is studied. It is shown that if the system has covering relations with weak Lyapunov condition determined by a transition matrix, there exists a sequence of compact invariant sets restricted to which the system is topologically conjugate to the two-sided subshift of finite type induced by the transition matrix. Moreover, if the systems have covering relations with exponential dichotomy and small Lipschitz perturbations, then there is a constructive verification proof of the weak Lyapunov condition, and so topological dynamics of these systems are fully understood by symbolic representations. In addition, the tolerance of Lipschitz perturbation can be characterised by the dichotomy tuple. Here, the weak Lyapunov condition is adapted from [12, 21, 15] and the exponential dichotomy is from [2].