Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings

Hironori Inoue, Daisuke Takahashi, Junta Matsukidaira

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    We propose discrete mappings of second order that have a discrete analogue of Lyapunov function. The mappings are extensions of the integrable Quispel-Roberts-Thompson (QRT) mapping, and a discrete Lyapunov function of the mappings is identical to an explicit conserved quantity of the QRT mapping. Moreover we can obtain a differential and an ultradiscrete limit of the mappings preserving the existence of Lyapunov function. We also give applications of a mapping with an adjusted parameter, a probabilistic mapping and coupled mappings.

    Original languageEnglish
    Pages (from-to)22-30
    Number of pages9
    JournalPhysica D: Nonlinear Phenomena
    Volume217
    Issue number1
    DOIs
    Publication statusPublished - 2006 May 1

    Fingerprint

    discrete functions
    Liapunov functions
    Lyapunov functions
    Lyapunov Function
    Conserved Quantity
    preserving
    analogs

    Keywords

    • Discrete mapping
    • Integrable system
    • Lyapunov function
    • Ultradiscrete equation

    ASJC Scopus subject areas

    • Applied Mathematics
    • Statistical and Nonlinear Physics

    Cite this

    Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings. / Inoue, Hironori; Takahashi, Daisuke; Matsukidaira, Junta.

    In: Physica D: Nonlinear Phenomena, Vol. 217, No. 1, 01.05.2006, p. 22-30.

    Research output: Contribution to journalArticle

    @article{edb508956bd24eb9aa9619f61e6b7686,
    title = "Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings",
    abstract = "We propose discrete mappings of second order that have a discrete analogue of Lyapunov function. The mappings are extensions of the integrable Quispel-Roberts-Thompson (QRT) mapping, and a discrete Lyapunov function of the mappings is identical to an explicit conserved quantity of the QRT mapping. Moreover we can obtain a differential and an ultradiscrete limit of the mappings preserving the existence of Lyapunov function. We also give applications of a mapping with an adjusted parameter, a probabilistic mapping and coupled mappings.",
    keywords = "Discrete mapping, Integrable system, Lyapunov function, Ultradiscrete equation",
    author = "Hironori Inoue and Daisuke Takahashi and Junta Matsukidaira",
    year = "2006",
    month = "5",
    day = "1",
    doi = "10.1016/j.physd.2006.03.004",
    language = "English",
    volume = "217",
    pages = "22--30",
    journal = "Physica D: Nonlinear Phenomena",
    issn = "0167-2789",
    publisher = "Elsevier",
    number = "1",

    }

    TY - JOUR

    T1 - Discrete mappings with an explicit discrete Lyapunov function related to integrable mappings

    AU - Inoue, Hironori

    AU - Takahashi, Daisuke

    AU - Matsukidaira, Junta

    PY - 2006/5/1

    Y1 - 2006/5/1

    N2 - We propose discrete mappings of second order that have a discrete analogue of Lyapunov function. The mappings are extensions of the integrable Quispel-Roberts-Thompson (QRT) mapping, and a discrete Lyapunov function of the mappings is identical to an explicit conserved quantity of the QRT mapping. Moreover we can obtain a differential and an ultradiscrete limit of the mappings preserving the existence of Lyapunov function. We also give applications of a mapping with an adjusted parameter, a probabilistic mapping and coupled mappings.

    AB - We propose discrete mappings of second order that have a discrete analogue of Lyapunov function. The mappings are extensions of the integrable Quispel-Roberts-Thompson (QRT) mapping, and a discrete Lyapunov function of the mappings is identical to an explicit conserved quantity of the QRT mapping. Moreover we can obtain a differential and an ultradiscrete limit of the mappings preserving the existence of Lyapunov function. We also give applications of a mapping with an adjusted parameter, a probabilistic mapping and coupled mappings.

    KW - Discrete mapping

    KW - Integrable system

    KW - Lyapunov function

    KW - Ultradiscrete equation

    UR - http://www.scopus.com/inward/record.url?scp=33646167059&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=33646167059&partnerID=8YFLogxK

    U2 - 10.1016/j.physd.2006.03.004

    DO - 10.1016/j.physd.2006.03.004

    M3 - Article

    AN - SCOPUS:33646167059

    VL - 217

    SP - 22

    EP - 30

    JO - Physica D: Nonlinear Phenomena

    JF - Physica D: Nonlinear Phenomena

    SN - 0167-2789

    IS - 1

    ER -