The Estimation For The Topological Entropy Of Non-autonomous Dynamical Systems

In this paper, the topological entropy of non-autonomous dynamical systems isstudied. The bounds of the topological entropy for several particular nonautonomoussystems, such as affine transformations on torus and Lipschitz maps on finite dimen-sional compact metric space, are obtained. The main results are as follows:1. For the sequence of Lipschitz maps on finite dimensional compact metricspace, we havein which D(X) is the ball dimension of X, L(fi) is the Lipschitz constant of fi.2. For the sequence of equicontinuous expanding endomorphisms on k-dimensionaltorus, we havei√n whichλi( 1),λ(i 2),...,λ(i k)is the eigenvalue of Ai,Λ(i 1)is the maximum eigenvalue ofAiAiT , i∈N.