Global Bifurcations of Periodic Solutions of Hénon–Heiles System Via Degree for S1-Equivariant Orthogonal Maps-Reference-Cited by-同舟云学术

Global Bifurcations of Periodic Solutions of Hénon–Heiles System Via Degree for S1-Equivariant Orthogonal Maps

Published:1998-11 Issue:08 Volume:10 Page:1125-1146
ISSN:0129-055X
Container-title:Reviews in Mathematical Physics
language:en
Short-container-title:Rev. Math. Phys.

Author:

Maciejewski Andrzej¹,Rybicki Sławomir²

Affiliation:

1. Toruń Centre for Astronomy, Nicolaus Copernicus University, PL-87-100 Toruń, ul. Gagarina 11, Poland

2. Faculty of Mathematics and Informatics, Nicolaus Copernicus University, PL-87-100 Toruń, ul. Chopina 12/18, Poland

Abstract

In this article we investigate global bifurcations of non-stationary periodic solutions of autonomous Hamiltonian systems. As the main tool we use the degree theory for S 1-equivariant orthogonal maps (see [24]–[26]). In order to illustrate our abstract results, we study global bifurcations of periodic solutions of the famous Hénon–Heiles Hamiltonian system.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129055X98000379

Reference19 articles.

1. Multiple positive fixed points of asymptotically linear maps

2. Saddle points and multiple solutions of differential equations

3. Periodic solutions of asymptotically linear Hamiltonian systems

4. Bi-Hamiltonian formulation of the Hénon-Heiles system and its multidimensional extensions

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