Multiple Periodic Solutions and Fractal Attractors of Differential Equations with n-Valued Impulses

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73602184" target="_blank" >RIV/61989592:15310/20:73602184 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mdpi.com/2227-7390/8/10/1701/htm" target="_blank" >https://www.mdpi.com/2227-7390/8/10/1701/htm</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math8101701" target="_blank" >10.3390/math8101701</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Multiple Periodic Solutions and Fractal Attractors of Differential Equations with n-Valued Impulses

Popis výsledku v původním jazyce

Ordinary differential equations with n-valued impulses are examined via the associated Poincare translation operators from three perspectives: (i) the lower estimate of the number of periodic solutions on the compact subsets of Euclidean spaces and, in particular, on tori; (ii) weakly locally stable (i.e., non-ejective in the sense of Browder) invariant sets; (iii) fractal attractors determined implicitly by the generating vector fields, jointly with Devaney&apos;s chaos on these attractors of the related shift dynamical systems. For (i), the multiplicity criteria can be effectively expressed in terms of the Nielsen numbers of the impulsive maps. For (ii) and (iii), the invariant sets and attractors can be obtained as the fixed points of topologically conjugated operators to induced impulsive maps in the hyperspaces of the compact subsets of the original basic spaces, endowed with the Hausdorff metric. Five illustrative examples of the main theorems are supplied about multiple periodic solutions (Examples 1-3) and fractal attractors (Examples 4 and 5).

Název v anglickém jazyce

Multiple Periodic Solutions and Fractal Attractors of Differential Equations with n-Valued Impulses

Popis výsledku anglicky

Ordinary differential equations with n-valued impulses are examined via the associated Poincare translation operators from three perspectives: (i) the lower estimate of the number of periodic solutions on the compact subsets of Euclidean spaces and, in particular, on tori; (ii) weakly locally stable (i.e., non-ejective in the sense of Browder) invariant sets; (iii) fractal attractors determined implicitly by the generating vector fields, jointly with Devaney&apos;s chaos on these attractors of the related shift dynamical systems. For (i), the multiplicity criteria can be effectively expressed in terms of the Nielsen numbers of the impulsive maps. For (ii) and (iii), the invariant sets and attractors can be obtained as the fixed points of topologically conjugated operators to induced impulsive maps in the hyperspaces of the compact subsets of the original basic spaces, endowed with the Hausdorff metric. Five illustrative examples of the main theorems are supplied about multiple periodic solutions (Examples 1-3) and fractal attractors (Examples 4 and 5).

Druh

J_SC - Článek v periodiku v databázi SCOPUS

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

Mathematics

ISSN

2227-7390

e-ISSN

—

Svazek periodika

8

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

21

Strana od-do

"1701-1"-"1701-21"

Kód UT WoS článku

000586911300001

EID výsledku v databázi Scopus

2-s2.0-85092915848