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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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 &quot;nonparametric&quot; 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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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 &quot;nonparametric&quot; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

ISSN

0218-1274

e-ISSN

1793-6551

Svazek periodika

33

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

13

Strana od-do

"2350113-1"-"2350113-13"

Kód UT WoS článku

001043906900014

EID výsledku v databázi Scopus

2-s2.0-85168768476