IP7 ~ Tuesday, May 23, 1995 ~ 8:30 AM
Onset of Spatio-Temporal Chaos in Unbounded Lattice Models
The speaker will demonstrate spatial-temporal chaos in lattice models of unbounded multi-dimensional and multi-component media. These models are associated with some well-known partial differential equations such as nonlinear diffusion equation, Ginzburg-Landau equation, and the Fitz-Hugh Nagumo equation. They also can serve as phenomenological models for some physical processes in media. The unboundedness of the medium implies the important fact that the lattice models admit two group actions generated by time translations (i.e. by the evolution operator) and space translations. The speaker will discuss different mechanisms, which have been recently discovered, that cause the appearance of chaotic behavior. The first is associated with chains of weakly interacting one-dimensional or multi-dimensional mappings that features some hyperbolic behaviour. The second is generated by a finite-dimensional dynamics that handles essentially the behavior of solutions of extended systems with dissipation and energy pumping.
Yakov B. Pesin
Department of Mathematics, Pennsylvania State University