Topological Methods in Nonlinear Analysis

Conley index over the base morphism for multivalued discrete dynamical systems

Kinga Stolot

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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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 29, Number 1 (2007), 163-180.

Dates
First available in Project Euclid: 13 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1463144891

Mathematical Reviews number (MathSciNet)
MR2308220

Zentralblatt MATH identifier
1130.37009

Citation

Stolot, Kinga. Conley index over the base morphism for multivalued discrete dynamical systems. Topol. Methods Nonlinear Anal. 29 (2007), no. 1, 163--180. https://projecteuclid.org/euclid.tmna/1463144891


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References

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