Chaotic zone in the Bogdanov-Takens bifurcation for diffeomorphisms

被引：0
|
作者：
Gelfreich, V [1 ]
机构：
[1] Free Univ Berlin, Inst Math 1, D-14195 Berlin, Germany
来源：
ANALYSIS AND APPLICATIONS - ISAAC 2001 | 2003年 / 10卷
关键词：
Bogdanov-Takens bifurcation; homoclinic orbits; exponentially small phenomena;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a two-parametric analytic family of diffeomorphisms near the Bogdanov-Takens bifurcation. It is known that if the parameters belong to a homoclinic zone, the map has homoclinic points. The width of the homoclinic zone is exponentially small. We derive an asymptotic formula for the width of the homoclinic zone. An analytic invariant associated with a parabolic fixed point is an important ingredient of this formula. The proof of the asymptotic formula is not complete. Additionally we provide results of computations of the invariant for model families.
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收藏
页码：187 / 197
页数：11
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