Stability islands in the vicinity of separatrices of near-integrable symplectic maps

被引：0

作者：

Simo, Carles ^{[1
]}

Treschev, Dmitri ^{[2
]}

机构：

[1] Univ Barcelona, Dept Matemat Aplicada & Anal, E-08007 Barcelona, Spain

[2] VA Steklov Math Inst, Moscow 119991, Russia

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2008年 / 10卷 / 2-3期

关键词：

area preserving maps; stability islands; lobes defined by invariant manifold; separatrix maps;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss the problem of existence of elliptic periodic trajectories inside lobes bounded by segments of stable and unstable separatrices of a hyperbolic fixed point. We show that such trajectories generically exist in symplectic maps arbitrary close to integrable ones. Elliptic periodic trajectories as a rule, generate stability islands. The area of such an island is of the same order as the lobe area, but the quotient of areas can be very small. Numerical examples are included.

引用

页码：681 / 698

页数：18

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