Weak Index Pairs and the Conley Index for Discrete Multivalued Dynamical Systems

Abstract

Motivated by the problem of reconstructing dynamics from samples, we revisit the Conley index theory for discrete multivalued dynamical systems [T. Kaczynski and M. Mrozek, Topology Appl., 65 (1995), pp. 83--96]. We introduce a new, less restrictive definition of the isolating neighborhood. It turns out that then the main tool for the construction of the index, i.e., the index pair, is no longer useful. In order to overcome this obstacle we use the concept of weak index pairs.