Separation of variables for the generalized Henon-Heiles system and system with quartic potential

Abstract

We consider two well-known integrable systems on the plane using the concept of natural Poisson bivectors on Riemaninan manifolds. Geometric approach to construction of variables of separation and separated relations for the generalized Henon-Heiles system and the generalized system with quartic potential is discussed in detail.

arXiv comment9 pages, LaTeX with AMS fonts

References in corpus (6)

• Quasi-point separation of variables for the Henon-Heiles system and a system with quartic potential
• New variables of separation for particular case of the Kowalevski top
• On the generalized integrable Chaplygin system
• On natural Poisson bivectors on the sphere
• Lax representation for two--particle dynamics splitting on two tori
• Towards a classification of natural bi-hamiltonian systems

Cited by in corpus (3)

• On bi-integrable natural Hamiltonian systems on the Riemannian manifolds
• Generalized Lenard Chains, Separation of Variables and Superintegrability
• On one integrable system with a cubic first integral