On the existence of closed magnetic geodesics via symplectic reduction

DOI10.1007/s11784-018-0528-3zbMath1385.37071arXiv1607.04098OpenAlexW2963063771WikidataQ130208029 ScholiaQ130208029MaRDI QIDQ1742573

Luca Asselle, Felix Schmäschke

Publication date: 11 April 2018

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.04098

zbMATH Keywords

periodic orbitsymplectic reductionRabinowitz action functionalmagnetic flowMañé critical value

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Momentum maps; symplectic reduction (53D20)

Related Items

Existence of curves with constant geodesic curvature in a Riemannian 2-sphere, Floer trajectories and stabilizing divisors, On geodesic flows with symmetries and closed magnetic geodesics on orbifolds

Cites Work

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• Lectures on the free period Lagrangian action functional
• Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level
• Closed orbits of a charge in a weakly exact magnetic field
• Infinitely many periodic orbits in non-exact oscillating magnetic fields on surfaces with genus at least two for almost every low energy level
• Helicity and the Mañé critical value
• Periodic orbits of twisted geodesic flows and the Weinstein-Moser theorem
• Symplectic topology of Mañé's critical values
• Hamiltonian dynamics on convex symplectic manifolds
• New generalizations of Poincaré's geometric theorem
• Periodic solutions of Hamiltonian system on a prescribed energy surface
• Closed nonself-intersecting extremals of multivalued functionals
• A contact condition for \(p\)-codimensional submanifolds of a symplectic manifold \((2\leq p\leq n)\)
• Momentum maps and Hamiltonian reduction
• Floer homology in disk bundles and symplectically twisted geodesic flows
• On the existence of three closed magnetic geodesics for subcritical energies
• On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus
• Applications of Hofer's geometry to Hamiltonian dynamics
• The Palais-Smale condition on contact type energy levels for convex Lagrangian systems
• Relations between homology and homotopy groups of spaces. II
• Relations between homology and homotopy groups of spaces
• On the existence of infinitely many closed geodesics on non-compact manifolds
• LEAF-WISE INTERSECTIONS AND RABINOWITZ FLOER HOMOLOGY
• A smooth pseudo-gradient for the Lagrangian action functional
• The Hamiltonian formalism and a many-valued analogue of Morse theory
• Periodic solutions of hamiltonian systems
• A.D. Alexandrov spaces with curvature bounded below
• Generalized Rabinowitz Floer Homology and Coisotropic Intersections
• On the Conley conjecture for Reeb flows
• The Lusternik–Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles
• Existence of periodic solutions of Hamiltonian systems on almost every energy surface
• Geodesics on a two-dimensional Riemannian manifold with periodic coefficients
• Riemannian geometry.