ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 58, 34 Gidea, Marian, Loyola University of Chicago Non-Smooth Dynamical Systems that Exhibit Hyperbolic Behavior The Conley index theory can be viewed as an extension of Morse theory to arbitrary flows defined on locally compact metric spaces. We construct a new Conley index for non-invariant sets . We use this index to study the asymptotic behavior of some orbits relative to the reference orbit of the non-invariant set and to detect symbolic dynamics. We extend the concept of hyperbolic system to non-smooth dynamical systems in terms of this new Conley index. Stability of the system, shadowing lemma and existence of Markov approximations can be proved under some topological assumptions. Reference: M. Gidea, The Conley Index and Countable Decompositions of Invariant Sets, Banach Center Publications, to appear.