Lyapunov–Schmidt Approach to Studying Homoclinic Splitting in Weakly Perturbed Lagrangian and Hamiltonian Systems

被引：0

作者：

A. M. Samoilenko

A. K. Prykarpats'kyi

V. H. Samoilenko

机构：

[1] Ukrainian Academy of Sciences,Institute of Mathematics

[2] Lviv; University of Mining and Metallurgy,Institute for Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences

[3] Shevchenko Kiev University,undefined

来源：

Ukrainian Mathematical Journal | 2003年 / 55卷 / 1期

关键词：

Hamiltonian System; Geometric Structure; Critical Manifold; Weakly Perturb; Schmidt Approach;

D O I：

10.1023/A:1025072619144

中图分类号：

学科分类号：

摘要：

We analyze the geometric structure of the Lyapunov–Schmidt approach to studying critical manifolds of weakly perturbed Lagrangian and Hamiltonian systems.

引用

页码：82 / 92

页数：10

共 5 条

[1]

Wiggings S.(1998)Global bifurcation and chaos Appl. Math. Sci. 73 370-1681

[2]

Samoilenko A. M.(1993)The Poincaré - Mel'nikov geometric analysis of the transversal splitting of separatrix manifolds for slowly perturbed nonlinear dynamical systems Ukr. Mat. Zh. 45 1668-52

[3]

Tymchyshyn O. Y.(1963)On the center stability under periodic perturbations Proc. Moscow Math. Soc 2 3-undefined

[4]

Prykarpats'kyi A. K.(undefined)undefined undefined undefined undefined-undefined

[5]

Mel'nikov V. K.(undefined)undefined undefined undefined undefined-undefined

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