Pathology in dynamical systems. III: Analytic Hamiltonians

DOI10.1016/0022-0396(80)90085-6zbMath0421.58015OpenAlexW2086642370MaRDI QIDQ1133222

Richard C. Churchill, David L. Rod

Publication date: 1980

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(80)90085-6

zbMATH Keywords

hyperbolic periodic orbitsHenon-Heiles Hamiltoniannondegenerate homoclinic and heteroclinic orbitsreal analytic Hamiltonian systems with two degrees of freedomSmale horseshoe mapping

Mathematics Subject Classification ID

Related Items (18)

Bifurcations into pathology for Hamiltonian systems ⋮ Geometrical aspects of Ziglin's non-integrability theorem for complex Hamiltonian systems ⋮ Homoclinic and heteroclinic orbits of reversible vectorfields under perturbation ⋮ Homoclinic bifurcations and the area-conserving Henon mapping ⋮ Equatorial dynamics of charged particles in planetary magnetospheres ⋮ The noisy shift map ⋮ Complexity in spatio-temporal dynamics ⋮ A consequence of the growth of rotation sets for families of diffeomorphisms of the torus ⋮ Horseshoes in the measure-preserving Hénon map ⋮ Conservative dynamics: unstable sets for saddle-center loops. ⋮ Horseshoes for autonomous Hamiltonian systems using the Melnikov integral ⋮ Symbolic dynamics for the Hénon-Heiles Hamiltonian on the critical level ⋮ Shooting methods and topological transversality ⋮ Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics ⋮ Proof of non-integrability for the Hénon-Heiles Hamiltonian near an exceptional integrable case ⋮ Chaos in a modified Hénon-Heiles system describing geodesics in gravitational waves ⋮ Global surfaces of section for dynamically convex Reeb flows on lens spaces ⋮ On the multiplicity of periodic orbits and homoclinics near critical energy levels of Hamiltonian systems in $\mathbb {R}^4$

Cites Work

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• The analytic invariants of an area-preserving mapping near a hyperbolic fixed point
• On the generalization of a theorem of A. Liapounoff
• Reversible Diffeomorphisms and Flows
• Examples of Nonintegrable Analytic Hamiltonian Vector Fields with no Small Divisors

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