Andres Jan: Topological entropy for impulsive differential equations. (2020)
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Abstract
A positive topological entropy is examined for impulsive differential equations via the associated Poincaré translation operators on compact subsets of Euclidean spaces and, in particular, on tori. We will show the conditions under which the impulsive mapping has the forcing property in the sense that its positive topological entropy implies the same for its composition with the Poincaré translation operator along the trajectories of given systems. It allows us to speak about chaos for impulsive differential equations under consideration. In particular, on tori, there are practically no implicit restrictions for such a forcing property. Moreover, the asymptotic Nielsen number (which is in difference to topological entropy a homotopy invariant) can be used there effectively for the lower estimate of topological entropy. Several illustrative examples are supplied.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2020 |
| Number: | 68 |
| ISSN: | 1417-3875 |
| Number of Pages: | 15 |
| Language: | English |
| DOI: | 10.14232/ejqtde.2020.1.68 |
| Uncontrolled Keywords: | Differenciálegyenlet |
| Additional Information: | Bibliogr.: p. 13-15. ; összefoglalás angol nyelven |
| Date Deposited: | 2021. Nov. 05. 12:50 |
| Last Modified: | 2021. Nov. 05. 12:50 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/73629 |
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