Applications of the Conley Index . . . (MS7)

MS7 ~ Sunday, May 21, 1995 ~ 2:30 PM

Applications of the Conley Index

Each isolated invariant set of a dynamical system has a Conley index which is stable with respect to small perturbations of the system. A geometric object called an isolating block is sometimes used to compute the index. The index is used to show that certain invariant sets continue to exist as parameters are varied. The index is also used or to show that heteroclinic orbits exist between invariant sets. In the context of reaction diffusion equations, the Conley index has been used to extablish the existence of traveling wave solutions. Recent research has extended the use of the Conley index to discrete dynamical systems. The speakers will provide an overview of some recent work on applications of the Conley index.

Organizer: Robert W. Easton, University of Colorado, Boulder

Isolating Blocks and the Conley Index: Robert W. Easton, Organizer
Numerics and the Conley Index: Konstantin Mischaikow, Georgia Institute of Technology
A Qualitative Singular Perturbation Theorem: James Reineck, State University of New York, Buffalo
Reconstructing Global Dynamics from the Conley Index: Chris McCord, University of Cincinnati

3/15/95