High-frequency chaotic solutions for a slowly varying dynamical system

Patricio Felmer, Salomé Martínez, Kazunaga Tanaka

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    In this article we study the asymptotic dynamics of highly oscillatory solutions for the unbalanced Allen-Cahn equation with a slowly varying coefficient. We describe the underlying structure of these solutions through a function we call the adiabatic profile, which accounts for the asymptotic area covered by the solutions in the phase space. In finite intervals, we construct solutions given any adiabatic profile. In the case of a periodic coefficient we show that the system has chaotic behavior by constructing high-frequency complex solutions which can be characterized by a bi-infinite sequence of real numbers in [c1,c2] ∪ {0} (0 <c1 <c 2).

    Original languageEnglish
    Pages (from-to)379-407
    Number of pages29
    JournalErgodic Theory and Dynamical Systems
    Volume26
    Issue number2
    DOIs
    Publication statusPublished - 2006 Apr

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    Dynamical systems
    Dynamical system
    Allen-Cahn Equation
    Oscillatory Solution
    Varying Coefficients
    Periodic Coefficients
    Chaotic Behavior
    Phase Space
    Interval
    Chaotic systems
    Profile

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Cite this

    High-frequency chaotic solutions for a slowly varying dynamical system. / Felmer, Patricio; Martínez, Salomé; Tanaka, Kazunaga.

    In: Ergodic Theory and Dynamical Systems, Vol. 26, No. 2, 04.2006, p. 379-407.

    Research output: Contribution to journalArticle

    Felmer, Patricio ; Martínez, Salomé ; Tanaka, Kazunaga. / High-frequency chaotic solutions for a slowly varying dynamical system. In: Ergodic Theory and Dynamical Systems. 2006 ; Vol. 26, No. 2. pp. 379-407.
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