摘要
Suppose that X is a compact metric space and f: X→X is continuous. The problem of the estimation for topological entropy ent(f) is important and difficult in the theory of dynamical systems, and its progress is hardly known. For example, so far as we know, no necessary and sufficient condition for vanishing of topological entropy has been obtained for general case. Recently, we have obtained the following results by the method of ergodic theory.
