Bifurcations of invariant manifolds in the generalized Hénon-Heiles system

DOI10.1016/0167-2789(89)90236-4zbMath0689.58014OpenAlexW2030394189MaRDI QIDQ581894

Lyubomir Gavrilov

Publication date: 1989

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(89)90236-4

zbMATH Keywords

invariant manifoldsbifurcationsHénon-Heiles Hamiltonian

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (12)

Bifurcation analysis of the motion of a cylinder and a point vortex in an ideal fluid ⋮ Bifurcation diagrams and Fomenko's surgery on Liouville tori of the Kolossoff potential $U=\rho+(1/\rho)-k\cos\phi$ ⋮ Elliptic Baker–Akhiezer functions and an application to an integrable dynamical system ⋮ The Hénon-Heiles system ⋮ Elliptic solutions and blow-up in an integrable Hénon–Heiles system ⋮ Noncompact bifurcations of integrable dynamic systems ⋮ Exact Solutions in the Invariant Manifolds of the Generalized Integrable Hénon–Heiles System and Exact Traveling Wave Solutions of Klein–Gordon–Schrödinger Equations ⋮ The generalized Hénon-Heiles system, abelian surfaces and algebraic complete integrability ⋮ Normal form methods for symbolic creation of approximate solutions of nonlinear dynamical systems ⋮ Separability and Lax pairs for Hénon–Heiles system ⋮ Unnamed Item ⋮ Exact solutions for a class of integrable Hénon–Heiles-type systems

Cites Work

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• Bifurcation of common levels of first integrals of the Kovalevskaya problem
• A unified approach to Painlevé expansions
• The Kowalewski and Hénon-Heiles motions as Manakov geodesic flows on SO(4) - a two-dimensional family of Lax pairs
• Completely integrable systems, Euclidean Lie algebras, and curves
• Topology and mechanics. I
• Theta functions and non-linear equations
• Ample Divisors on Abelian Surfaces
• Analytic structure of the Henon–Heiles Hamiltonian in integrable and nonintegrable regimes

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