High-frequency chaotic solutions for a slowly varying dynamical system

Patricio Felmer*, Salomé Martínez, Kazunaga Tanaka

*この研究の対応する著者

研究成果: Article査読

5 被引用数 (Scopus)

抄録

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).

本文言語English
ページ(範囲)379-407
ページ数29
ジャーナルErgodic Theory and Dynamical Systems
26
2
DOI
出版ステータスPublished - 2006 4月 1

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

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