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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

  • 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

  • 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