一个二维分段光滑映象中的边界激变

BOUNDARY CRISIS IN A2D PIECE-WISE SMOOTH MAP

解析地讨论一个冲击振子模型中的边界激变特征 ,证明了这类分段光滑二维映象中激变的生存时间标度律为τ ε-γ,而γ =ln|β2 |ln|β1β2 |(β1,β2 分别是混沌吸引子吸引域边界上鞍点的不稳定和稳定本征值 ) ,这与处处光滑二维映象中相应的规律完全不同 .

This paper analytically discusses the characteristics of boundary crisis in a model of impact oscillator,and proves that the scaling behavior of the life time after crisis follows the rule τ ε\+\{-γ\} and γ=ln|β 2|ln|β 1β\-2|.Here β 1 and β 2 are the unstable and stable eigenvalues,respectively,of a saddle node on the basin boundary of a chaotic attractor.This rule is completely different from that in everywhere\|smooth maps.