Parametric topological entropy and differential equations with time–dependent impulses

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73612503" target="_blank" >RIV/61989592:15310/22:73612503 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022039622000948" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039622000948</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2022.02.008" target="_blank" >10.1016/j.jde.2022.02.008</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Parametric topological entropy and differential equations with time–dependent impulses

Popis výsledku v původním jazyce

Stimulated by a multiple solvability of periodic boundary value problems to differential equations with time–dependent impulses, we recall a related definition of parametric topological entropy for a sequence of continuous self–maps on a compact metric space. The main simple idea consists in replacing the iterates of a single map by the compositions of several various maps. For an equicontinuous countable family of self–maps on a compact connected polyhedron, we develop a lower estimate of this entropy in terms of the asymptotic Nielsen numbers of their compositions. This Ivanov–type equality is then applied, via the associated Poincaré translation operators, to differential equations with time–dependent impulses on tori. If the supporting space differs from a homotopy type of tori, then the situation becomes more delicate. Nevertheless, on compact connected punctured surfaces, we are still able to apply in a similar way the Artin braid group theory to planar differential equations with a finite number of homeomorphic impulses. Some further possibilities are commented in remarks and several illustrative examples are supplied.

Název v anglickém jazyce

Parametric topological entropy and differential equations with time–dependent impulses

Popis výsledku anglicky

Stimulated by a multiple solvability of periodic boundary value problems to differential equations with time–dependent impulses, we recall a related definition of parametric topological entropy for a sequence of continuous self–maps on a compact metric space. The main simple idea consists in replacing the iterates of a single map by the compositions of several various maps. For an equicontinuous countable family of self–maps on a compact connected polyhedron, we develop a lower estimate of this entropy in terms of the asymptotic Nielsen numbers of their compositions. This Ivanov–type equality is then applied, via the associated Poincaré translation operators, to differential equations with time–dependent impulses on tori. If the supporting space differs from a homotopy type of tori, then the situation becomes more delicate. Nevertheless, on compact connected punctured surfaces, we are still able to apply in a similar way the Artin braid group theory to planar differential equations with a finite number of homeomorphic impulses. Some further possibilities are commented in remarks and 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

2022

Kód důvěrnosti údajů

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

Název periodika

JOURNAL OF DIFFERENTIAL EQUATIONS

ISSN

0022-0396

e-ISSN

1090-2732

Svazek periodika

317

Číslo periodika v rámci svazku

APR

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

365-386

Kód UT WoS článku

000820181800002

EID výsledku v databázi Scopus

2-s2.0-85124494663