Stability and invariance of multivalued iterated function systems

Rok, strany: 2003, 393 - 405

We provide a definition of an attractor to a multivalued iterated function system (IFS) modelled on previous ones existing in the literature (e.g. [Hale, J. K.: Asymptotic Behavior of Dissipative Systems. Math. Surveys Monographs 25, Amer. Math. Soc., Providence, RI, 1988]). Such an attractor expressing asymptotic behaviour of a system does not need to be invariant. Then, as a remedy there serves the uniform Hausdorff upper semicontinuity. It was recently shown that condensing multifunctions possess a maximal invariant set which is compact. The theorem ensuring the existence of attractors considered here also exploits compactness-like hypothesis slightly stronger than condensity, namely contractivity with respect to measure of noncompactness. Hence contractivity in measure and uniform Hausdorff upper semicontinuity together do guarantee existence of a compact attractor which is maximal invariant and unique. We also supply examples (e.g. unbounded attractor) and state further questions.

ISO 690:

Leśniak, K. 2003. Stability and invariance of multivalued iterated function systems. In Mathematica Slovaca, vol. 53, no.4, pp. 393-405. 0139-9918.

APA:

Leśniak, K. (2003). Stability and invariance of multivalued iterated function systems. Mathematica Slovaca, 53(4), 393-405. 0139-9918.