The equivariant Conley index and bifurcations of periodic solutions of Hamiltonian systems

DOI10.1017/S0143385700009354zbMath0694.58017OpenAlexW1964671737MaRDI QIDQ3469934

Andreas Floer, Eduard Zehnder

Publication date: 1988

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700009354

zbMATH Keywords

periodic solutions of Hamiltonian systems

Mathematics Subject Classification ID

Index theory and related fixed-point theorems on manifolds (58J20) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (7)

Multiplicity of periodic solutions to symmetric delay differential equations ⋮ A generalization of the Weinstein-Moser theorems on periodic orbits of a Hamiltonian system near an equilibrium ⋮ Equivariant Morse equation ⋮ Seiberg-Witten Floer spectra and contact structures ⋮ Equivariant Conley index in Hilbert spaces and applications to strongly indefinite problems ⋮ Subharmonics near an equilibrium point for Hamiltonian systems ⋮ Bifurcation theory for symmetric potential operators and the equivariant cup-length

Cites Work

• Unnamed Item
• Proof of the Arnold conjecture for surfaces and generalizations to certain Kähler manifolds
• Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems
• Normal modes for nonlinear Hamiltonian systems
• A refinement of the Conley index and an application to the stability of hyperbolic invariant sets
• Periodic orbits near an equilibrium and a theorem by Alan Weinstein
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations

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