THE LYAPUNOV - SCHMIDT APPROACH TO STUDYING HOMOCLINICS SPLITTING IN WEAKLY PERTURBED LAGRANGIAN AND HAMILTONIAN SYSTEMS

A. M. Samoilenko; A. K. Prykarpatsky; V. Hr. Samoylenko

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THE LYAPUNOV - SCHMIDT APPROACH TO STUDYING HOMOCLINICS SPLITTING IN WEAKLY PERTURBED LAGRANGIAN AND HAMILTONIAN SYSTEMS

机译：研究弱扰动拉格朗日系统和哈密顿系统的同伦分裂的LYAPUNOV-SCHMIDT方法。

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摘要

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

机译：我们分析了Lyapunov-Schmidt方法的几何结构，以研究弱扰动的Lagrangian和Hamilton系统的关键流形。

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来源
《Украинский математический журнал》 |2003年第1期|p.66-74|共9页
作者
A. M. Samoilenko; A. K. Prykarpatsky; V. Hr. Samoylenko;
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Inst. Math. Nat. Acad. Sci. Ukraine, Kyiv;

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正文语种 eng
中图分类数学;
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1. Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems (vol 114, pg 3, 1998) [J] . Rudnev M., Wiggins S. Physica, D. Nonlinear phenomena . 2000,第3a4期

机译：弱双曲型近可积分哈密顿系统中成千上万的小分离线分裂和晶须托之间的同斜联系（vol 114，pg 3，1998）
2. Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems [J] . Rudnev M., Wiggins S. Physica, D. Nonlinear phenomena . 1998,第1a2期

机译：弱双曲近可积分哈密顿系统中成千上万的小分离线分裂和晶须之间的同宿联系
3. Persistence of periodic solutions for higher order perturbed differential systems via Lyapunov-Schmidt reduction [J] . Candido Murilo R., Llibre Jaume, Novaes Douglas D. Nonlinearity . 2017,第9期

机译：通过Lyapunov-Schmidt减少持续高阶扰动差动系统的定期解决方案
4. GIANT ACCELERATION IN WEAKLY-PERTURBED SPACE-PERIODIC HAMILTONIAN SYSTEMS [C] . M. YU. ULEYSKY, D. V. MAKAROV Chaos, complexity and transport . 2008

机译：巨型加速在弱扰动的空间周期性哈密顿系统中
5. Homoclinic and Heteroclinic Orbits in Lagrangian Dynamical Systems. [D] . Yu, Guowei. 2013

机译：拉格朗日动力系统中的同宿和非斜轨道。
6. A matrix-based approach to solving the inverse Frobenius–Perron problem using sequences of density functions of stochastically perturbed dynamical systems [O] . Xiaokai Nie, Daniel Coca -1

机译：一种基于矩阵的方法使用随机扰动动力系统的密度函数序列来解决Frobenius-Perron逆问题
7. Exponentially small splitting for whiskered tori in Hamiltonian systems: Continuation of transverse homoclinic orbits [O] . Delshams Valdés, Amadeu, Gutiérrez Serrés, Pere 2003

机译：汉密尔顿系统中胡须托里的指数小分裂：横向同宿轨道的延续
8. Hamiltonians and Lagrangians for one-dimensional autonomous systems and dissipative systems. [R] . G. Lopez 1991

机译：哈密顿量和拉格朗日一维自治系统和耗散系统。

THE LYAPUNOV - SCHMIDT APPROACH TO STUDYING HOMOCLINICS SPLITTING IN WEAKLY PERTURBED LAGRANGIAN AND HAMILTONIAN SYSTEMS

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