On the existence of infinitely many periodic solutions to some problems of n‐body type

DOI10.1002/cpa.3160480404zbMath0820.58020OpenAlexW2069651758MaRDI QIDQ4837727

Susanna Terracini, Pietro Majer

Publication date: 17 September 1995

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.3160480404

zbMATH Keywords

Hamiltonian systemscritical point theorylack of compactnessLyusternik Schnirelman relative category

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) (n)-body problems (70F10) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (5)

Transitive decomposition of symmetry groups for the \(n\)-body problem ⋮ On the variational approach to the periodic \(n\)-body problem ⋮ Multiple closed orbits of fixed energy for \(N\)-body-type problems with gravitational potentials ⋮ Non-simultaneous collision periodic solutions for \(N\)-body problems ⋮ New proof and generalizations of the Demidowitsch–Schneider criterion

Cites Work

• Unnamed Item
• Critical points with lack of compactness and singular dynamical systems
• Periodic solutions to some \(N\)-body type problems: The fixed energy case
• Two variational methods on manifolds with boundary
• Noncollision periodic solutions to some singular dynamical systems with very weak forces
• Lusternik-Schnirelman theory on Banach manifolds
• Stability of critical points under small perturbations. I: Topological theory
• A Note on the Category of the Free Loop Space
• Conservative Dynamical Systems Involving Strong Forces
• A relative category and applications to critical point theory for strongly indefinite functionals

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