Parametric topological entropy and differential equations with time–dependent impulses

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Parametric topological entropy and differential equations with time–dependent impulses

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2022

Confidentiality

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

Name of the periodical

JOURNAL OF DIFFERENTIAL EQUATIONS

ISSN

0022-0396

e-ISSN

1090-2732

Volume of the periodical

317

Issue of the periodical within the volume

APR

Country of publishing house

US - UNITED STATES

Number of pages

22

Pages from-to

365-386

UT code for WoS article

000820181800002

EID of the result in the Scopus database

2-s2.0-85124494663