Perturbation of periodic manifolds of hamiltonian systems

DOI10.1090/S0002-9904-1971-12816-1zbMath0218.58006MaRDI QIDQ5622967

Alan Weinstein

Publication date: 1971

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Local and nonlocal bifurcation theory for dynamical systems (37G99)

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Congruences and canonical forms for a positive matrix: Application to the Schweinler–Wigner extremum principle ⋮ The Signorini perturbation scheme in an abstract setting ⋮ A separation bound for non-Hamiltonian differential equations with proper first integrals ⋮ Stability of periodic solutions of the \(N\)-vortex problem in general domains ⋮ The invariance of Poincaré's generating function for canonical transformations ⋮ Normal modes for nonlinear Hamiltonian systems ⋮ Generic multiparameter bifurcation from a manifold ⋮ Periodic orbits of a generalized Hénon–Heiles system

Cites Work

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• Symplectic manifolds and their Lagrangian submanifolds
• Nondegenerate critical manifolds
• Symplectic structures on Banach manifolds
• Regularization of kepler's problem and the averaging method on a manifold
• Generic Bifurcation of Periodic Points
• Closed Integral Curves in 3-Space and Isotopic Two-Dimensional Deformations