Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on Tori
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 eq...
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| Format: | Article |
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MDPI AG
2020-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/9/1602 |
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| author | Jan Andres Jerzy Jezierski |
| author_facet | Jan Andres Jerzy Jezierski |
| author_sort | Jan Andres |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T16:16:11Z |
| format | Article |
| id | doaj.art-ff7e37efb57e422680d68218d507b619 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T16:16:11Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ff7e37efb57e422680d68218d507b6192023-11-20T14:05:10ZengMDPI AGMathematics2227-73902020-09-0189160210.3390/math8091602Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on ToriJan Andres0Jerzy Jezierski1Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech RepublicDepartment of Informatics and Mathematics, Warsaw University of Life Sciences, Nowoursynowska 159, 02 757 Warsaw, PolandThe 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.https://www.mdpi.com/2227-7390/8/9/1602topological entropyasymptotic Nielsen numberadmissible pairscoincidencesimpulsive differential equations and inclusionspoincaré operators |
| spellingShingle | Jan Andres Jerzy Jezierski Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on Tori Mathematics topological entropy asymptotic Nielsen number admissible pairs coincidences impulsive differential equations and inclusions poincaré operators |
| title | Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on Tori |
| title_full | Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on Tori |
| title_fullStr | Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on Tori |
| title_full_unstemmed | Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on Tori |
| title_short | Ivanov’s Theorem for Admissible Pairs Applicable to Impulsive Differential Equations and Inclusions on Tori |
| title_sort | ivanov s theorem for admissible pairs applicable to impulsive differential equations and inclusions on tori |
| topic | topological entropy asymptotic Nielsen number admissible pairs coincidences impulsive differential equations and inclusions poincaré operators |
| url | https://www.mdpi.com/2227-7390/8/9/1602 |
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