Conley index over the base morphism for multivalued discrete dynamical systems. (English) Zbl 1130.37009

Stolot, Kinga

Topol. Methods Nonlinear Anal. 29, No. 1, 163-180 (2007).

Summary: We define an index of Conley type for a certain class of uppersemicontinuous multivalued dynamical systems, using techniques introduced by M. Mrozek, J. F. Reineck and R. Srzednicki [Trans. Am. Math. Soc. 352, No. 9, 4171–4194 (2000; Zbl 0967.37011)] 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 T. Kaczynski and M. Mrozek’s [Topology Appl. 65, No. 1, 83–96 (1995; Zbl 0843.54042)] index.

MSC:

37B30	Index theory for dynamical systems, Morse-Conley indices
54C60	Set-valued maps in general topology
37B35	Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems
54H20	Topological dynamics (MSC2010)

Citations:

Zbl 0967.37011; Zbl 0843.54042