The standard Sharkovsky cycle coexistence theorem applies to impulsive differential equations: Some notes and beyond
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
The standard Sharkovsky cycle coexistence theorem applies to impulsive differential equations: Some notes and beyond
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the American Mathematical Society
ISSN
0002-9939
e-ISSN
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Volume of the periodical
147
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
13
Pages from-to
1497-1509
UT code for WoS article
000458356700012
EID of the result in the Scopus database
2-s2.0-85061999002