Topological entropy for impulsive differential equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73603347" target="_blank" >RIV/61989592:15310/20:73603347 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.math.u-szeged.hu/ejqtde/p8927.pdf" target="_blank" >http://www.math.u-szeged.hu/ejqtde/p8927.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.14232/ejqtde.2020.1.68" target="_blank" >10.14232/ejqtde.2020.1.68</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Topological entropy for impulsive differential equations

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Topological entropy for impulsive differential equations

Popis výsledku anglicky

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.

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

2020

Kód důvěrnosti údajů

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

Název periodika

Electronic Journal of Qualitative Theory of Differential Equations

ISSN

1417-3875

e-ISSN

—

Svazek periodika

2020

Číslo periodika v rámci svazku

68

Stát vydavatele periodika

HU - Maďarsko

Počet stran výsledku

15

Strana od-do

1-15

Kód UT WoS článku

000601296600001

EID výsledku v databázi Scopus

2-s2.0-85098332816