On Symbolic Dynamics of One-Humped Maps of the Interval

Abstract

We present an explicit construction of minimal deterministic automata which accept the languages of L-R symbolic sequences of unimodal maps resp. arbitrarily close approximations thereof. They are used to study a recently introduced complexity measure of this language which we conjecture to be a new invariant under diffeomorphisms. On each graph corresponding to such an automaton, the evolution is a topological Markov chain which does not seem to correspond to a partition of the interval into a countable number of intervals. © 1988, Verlag der Zeitschrift für Naturforschung. All rights reserved.