00-387 Bastien Fernandez, Miaohua Jiang

Dynamics of Two Diffusively Coupled Unimodal Maps with Zero Topological Entropy (59K, ams-Latex) Oct 2, 00

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Abstract. The paper studies the dynamics of a coupled map lattice of two sites where the local map is a unimodal map for which the period of every periodic orbit is a power of two. With the help of the existence of nested subsets of the phase space and their forward invariance after some iterations, it is shown that every orbit passing such subsets is eventually periodic and the period is a power of two. A criterion for an orbit to visit a particular subset is given and a sufficient condition for the existence of periodic orbits satisfying this criterion is obtained.

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