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Keywords = asymptotic Nielsen number

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14 pages, 353 KiB  
Article
Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on Tori
by Jan Andres and Jerzy Jezierski
Mathematics 2020, 8(9), 1602; https://doi.org/10.3390/math8091602 - 17 Sep 2020
Cited by 7 | Viewed by 2222
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Topological Methods in Nonlinear Analysis)
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