## Hunseok Kang : The 16th COE Lecture Series

### CHAOS IN TRAVELING WAVES OF LATTICE SYSTEMS OF UNBOUNDED MEDIA

We describe coupled map lattices (CML) of unbounded media corresponding to some well-known evolution partial differential equations. Following Kaneko we view CML also as phenomenological models of the medium and present the dynamical system approach to study the global behavior of solutions of CML. In particular, we establish spatio-temporal chaos associated with the set of traveling wave solutions of CML as well as describe the dynamics of the evolution operator on this set. Several examples are given to illustrate the appearance of Smale horseshoes and the presence of the dynamics of Morse-Smale type.