Parametric Topological Entropy for Multivalued Maps and Differential Inclusions with Nonautonomous Impulses

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F23%3A73619697" target="_blank" >RIV/61989592:15310/23:73619697 - isvavai.cz</a>
Result on the web
<a href="https://www.worldscientific.com/doi/10.1142/S0218127423501122" target="_blank" >https://www.worldscientific.com/doi/10.1142/S0218127423501122</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0218127423501134" target="_blank" >10.1142/S0218127423501134</a>

Result language
angličtina
Original language name
Parametric Topological Entropy for Multivalued Maps and Differential Inclusions with Nonautonomous Impulses
Original language description
The main purpose of this paper is to investigate a parametric topological entropy for impulsive differential inclusions on tori. In this way, besides other matters, we would like to extend our recent results concerning impulsive differential equations as well as those on "nonparametric" topological entropy to impulsive differential inclusions. Parametric topological entropy, which is usually called a topological entropy for nonautonomous dynamical systems, is considered here via the compositions of associated multivalued Poincare translation operators with the single-valued time-dependent impulsive maps. On compact polyhedra and, in particular on tori, parametric topological entropy for families of admissible multivalued maps can be estimated from below by means Ivanov-type inequality in terms of the asymptotic Nielsen and Lefschetz numbers which are, unlike the topological entropy, homotopy invariants. In the scalar case, an effective criterion for a positive parametric topological entropy can be given by topological degree arguments for equi-continuous impulsive maps. In a single-valued nonparametric case, a positive topological entropy usually signifies topological chaos. Some simple illustrative examples are provided.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
ISSN
0218-1274
e-ISSN
1793-6551
Volume of the periodical
33
Issue of the periodical within the volume
9
Country of publishing house
SG - SINGAPORE
Number of pages
13
Pages from-to
"2350113-1"-"2350113-13"
UT code for WoS article
001043906900014
EID of the result in the Scopus database
2-s2.0-85168768476

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