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Open AccessArticle

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

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Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
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Department of Informatics and Mathematics, Warsaw University of Life Sciences, Nowoursynowska 159, 02 757 Warsaw, Poland
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(9), 1602; https://doi.org/10.3390/math8091602
Received: 15 August 2020 / Accepted: 15 September 2020 / Published: 17 September 2020
(This article belongs to the Special Issue Topological Methods in Nonlinear Analysis)
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. View Full-Text
Keywords: topological entropy; asymptotic Nielsen number; admissible pairs; coincidences; impulsive differential equations and inclusions; poincaré operators; coexistence of periodic solutions topological entropy; asymptotic Nielsen number; admissible pairs; coincidences; impulsive differential equations and inclusions; poincaré operators; coexistence of periodic solutions
MDPI and ACS Style

Andres, J.; Jezierski, J. Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on Tori. Mathematics 2020, 8, 1602.

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