On the Topological Entropy of Green Interval Maps

We investigate the topological entropy of a green interval map. Defining the complexity we estimate from above the topological entropy of a green interval map with a given complexity. The main result of the paper — stated in Theorem 0.2 — should be regarded as a completion of results of [4]. 0. Introduction and main result The purpose of this paper is to evaluate the topological entropy of green interval maps. The topological entropy provides a numerical measure for the complexity of such one-dimensional dynamical systems and our aim is to describe this complexity by means of combinatorics. A particular case of a system given by a P -monotone map fP for a green cycle P was investigated in [4]. Since a green interval map is not a uniform limit of such special green (Markov) maps, our Theorem 0.2 completes the result of [4]. 1991 Mathematics Subject Classification. 26A18, 37B40.