Periodic orbits and topological entropy of delayed maps - art. no. 046203

The periodic orbits of a nonlinear dynamical system provide valuable insigh t into the topological and metric properties of its chaotic attractors. In this paper we describe general properties of periodic orbits of dynamical s ystems with feedback delay. In the case of delayed maps, these properties e nable us to provide general arguments about the boundedness of the topologi cal entropy in the high delay limit. As a consequence, all the metric entro pies can be shown to be bounded in this limit. The general considerations a re illustrated in the cases of Bernoulli-like and Henon-like delayed maps.