TY - JOUR
T1 - High-frequency chaotic solutions for a slowly varying dynamical system
AU - Felmer, Patricio
AU - Martínez, Salomé
AU - Tanaka, Kazunaga
PY - 2006/4/1
Y1 - 2006/4/1
N2 - 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 1 2).
AB - 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 1 2).
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U2 - 10.1017/S0143385705000416
DO - 10.1017/S0143385705000416
M3 - Article
AN - SCOPUS:33645048455
SN - 0143-3857
VL - 26
SP - 379
EP - 407
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 2
ER -