Analytical determination of unstable periodic orbits in area preserving maps

DOI10.1016/0167-2789(87)90054-6zbMath0628.34043OpenAlexW2053735411MaRDI QIDQ1093074

B. George

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0167-2789(87)90054-6

zbMATH Keywords

Birkhoff normal formhomoclinic pointsunstable periodic orbit

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (9)

A review of the ``Third integral ⋮ Study of chaos in Hamiltonian systems via convergent normal forms ⋮ A semiclassical reversibility paradox in simple chaotic systems ⋮ Homoclinic and heteroclinic intersections for lemon billiards ⋮ Accurate determination of heteroclinic orbits in chaotic dynamical systems ⋮ Analytical invariant manifolds near unstable points and the structure of chaos ⋮ Extended convergence of normal forms around unstable equilibria ⋮ Bifurcations of mode equations: Spin waves ⋮ Semiclassical energy transition of driven chaotic systems: phase coherence on scar disks

Cites Work

• Unnamed Item
• Period doubling bifurcations and universality in conservative systems
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• The analytic invariants of an area-preserving mapping near a hyperbolic fixed point
• Numerical study of quadratic area-preserving mappings

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