Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on Tori

Jan Andres and Jerzy Jezierski
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Jan Andres: Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
Jerzy Jezierski: Department of Informatics and Mathematics, Warsaw University of Life Sciences, Nowoursynowska 159, 02 757 Warsaw, Poland

Mathematics, 2020, vol. 8, issue 9, 1-14

Abstract: The main aim of this article is two-fold: (i) to generalize into a multivalued setting the classical Ivanov theorem about the lower estimate of a topological entropy in terms of the asymptotic Nielsen numbers, and (ii) to apply the related inequality for admissible pairs to impulsive differential equations and inclusions on tori. In case of a positive topological entropy, the obtained result can be regarded as a nontrivial contribution to deterministic chaos for multivalued impulsive dynamics.

Keywords: topological entropy; asymptotic Nielsen number; admissible pairs; coincidences; impulsive differential equations and inclusions; poincaré operators; coexistence of periodic solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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