Conley index over the base morphism for multivalued discrete dynamical systems

Kinga Stolot

DOI: http://dx.doi.org/10.12775/TMNA.2007.007

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 [< i> The Conley index over a base< /i> , Trans.
Amer. Math. Soc. < b> 352< /b> (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 [< i> Conley index for discrete multi-valued dynamical systems< /i> ,
Topology Appl. < b> 65< /b> (1995), 83–96] index.

Keywords


Conley index; isolated invariant set; index pair; multivalued dynamical system

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