The standard Sharkovsky cycle coexistence theorem applies to impulsive differential equations: Some notes and beyond

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73595054" target="_blank" >RIV/61989592:15310/19:73595054 - isvavai.cz</a>

Výsledek na webu

<a href="https://obd.upol.cz/id_publ/333174940" target="_blank" >https://obd.upol.cz/id_publ/333174940</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/proc/14387" target="_blank" >10.1090/proc/14387</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The standard Sharkovsky cycle coexistence theorem applies to impulsive differential equations: Some notes and beyond

Popis výsledku v původním jazyce

We will show that, unlike usual (i.e., nonimpulsive) differential equations, the standard Sharkovsky cycle coexistence theorem applies easily to impulsive, scalar, ordinary differential equations. In fact, there is a one-to-one correspondence between the subharmonic solutions of given orders and periodic points of the same orders of the associated Poincaré translation operators, provided a uniqueness condition is satisfied. Despite the fact that the usage of the Poincaré operators in the context of impulsive differential equations is neither new, nor original, and that the application of the Sharkovsky celebrated theorem becomes in this way rather trivial, as far as we know, an appropriate theorem has not yet been formulated. As a by-product, the relationship of impulsive differential equations to deterministic chaos will also be clarified. In order to demonstrate the merit of the basic idea, some less trivial extensions for discontinuous and multivalued impulses will still be briefly done, along with indicating the situation in the lack of uniqueness.

Název v anglickém jazyce

The standard Sharkovsky cycle coexistence theorem applies to impulsive differential equations: Some notes and beyond

Popis výsledku anglicky

We will show that, unlike usual (i.e., nonimpulsive) differential equations, the standard Sharkovsky cycle coexistence theorem applies easily to impulsive, scalar, ordinary differential equations. In fact, there is a one-to-one correspondence between the subharmonic solutions of given orders and periodic points of the same orders of the associated Poincaré translation operators, provided a uniqueness condition is satisfied. Despite the fact that the usage of the Poincaré operators in the context of impulsive differential equations is neither new, nor original, and that the application of the Sharkovsky celebrated theorem becomes in this way rather trivial, as far as we know, an appropriate theorem has not yet been formulated. As a by-product, the relationship of impulsive differential equations to deterministic chaos will also be clarified. In order to demonstrate the merit of the basic idea, some less trivial extensions for discontinuous and multivalued impulses will still be briefly done, along with indicating the situation in the lack of uniqueness.

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

2019

Kód důvěrnosti údajů

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

Název periodika

Proceedings of the American Mathematical Society

ISSN

0002-9939

e-ISSN

—

Svazek periodika

147

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

13

Strana od-do

1497-1509

Kód UT WoS článku

000458356700012

EID výsledku v databázi Scopus

2-s2.0-85061999002