Conley index over the base morphism for multivalued discrete dynamical systems

Abstract

We define an index of Conley type for a certain class of uppersemicontinuous multivalued dynamical systems, using techniques introduced by Mrozek, Reineck and Srzednicki [The Conley index over a base, Trans. Amer. Math. Soc. 352 (2000), no. 9, 4171–4194] for the index over the base. We give the characterisation of the nontrivial index and present an example, proving that our index detects isolated invariant sets that are not detected by Kaczyński and Mrozek's [Conley index for discrete multi-valued dynamical systems, Topology Appl. 65 (1995), 83–96] index.