Study of chaos in Hamiltonian systems via convergent normal forms

DOI10.1016/0167-2789(95)00233-2zbMath0884.34044arXivchao-dyn/9606002OpenAlexW3100708868WikidataQ127348927 ScholiaQ127348927MaRDI QIDQ1905721

Werner M. Vieira, Alfredo M. Ozorio de Almeida

Publication date: 16 January 1996

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

Full work available at URL: https://arxiv.org/abs/chao-dyn/9606002

zbMATH Keywords

chaotic motionchaotic flowsaddle pointcylindrical topologyHénon-Heiles Hamiltonainhomoclinic interactionMoser's normal formstwo-degree Hamiltonian systems

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (6)

Analytical and numerical manifolds in a symplectic 4-D map ⋮ A review of the ``Third integral ⋮ Analytical invariant manifolds near unstable points and the structure of chaos ⋮ Extended convergence of normal forms around unstable equilibria ⋮ Universality in the chaotic dynamics associated with saddle-centers critical points ⋮ Bouncing braneworld cosmologies and initial conditions to inflation

Cites Work

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• Geometry and dynamics of stable and unstable cylinders in Hamiltonian systems
• On the numerical computation of Poincaré maps
• Analytical determination of unstable periodic orbits in area preserving maps
• The calculation of periodic trajectories
• Stability transitions for periodic orbits in Hamiltonian systems
• The Hénon-Heiles system revisited
• Index of a singular point of a vector field, the Petrovskii-Oleinik inequality, and mixed Hodge structures
• The analytic invariants of an area-preserving mapping near a hyperbolic fixed point
• On the generalization of a theorem of A. Liapounoff

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