The Hénon and Heiles Problem in Three Dimensions.-Reference-Cited by-同舟云学术

The Hénon and Heiles Problem in Three Dimensions.

Published:1998-06 Issue:06 Volume:08 Page:1215-1229
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Ferrer S.¹,Lara M.²,Palacián J.³,Juan J. F. San⁴,Viartola A.¹,Yanguas P.³

Affiliation:

1. Grupo de Mecánica Espacial, Universidad de Zaragoza, 50009 Zaragoza, Spain

2. Real Instituto y Observatorio de la Armada en San Fernando, 11110 San Fernando (Cádiz), Spain

3. Departamento de Matemática e Informática, Universidad Pública de Navarra, 31006 Pamplona, Spain

4. Departamento de Matemáticas y Computación, Universidad de la Rioja, 26004 Logroño, Spain

Abstract

The second part of a research on the Hénon and Heiles system in three dimensions is presented. We focus on motions around the origin, where the system may be treated as a case of three perturbed isotropic harmonic oscillators. It is the only Hamiltonian of the family of axially symmetric cubic potentials in 1–1–1 resonance, which needs at least order four in the normalization to reach the features of the system. The fourth order normalized system is analyzed, considering orbits at any inclination. We study and classify the relative equilibria of the system finding pitchfork, centre-saddle and cusp bifurcations in the reduced orbit space.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127498000954

Reference16 articles.

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2. On averaging, reduction, and symmetry in hamiltonian systems

3. The critical inclination in artificial satellite theory

4. Painting the Phase Space Portrait of an Integrable Dynamical System

5. Geometry of the bifurcations of the normalized reduced Henon–Heiles family

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