On the existence of periodic orbits for magnetic systems on the two-sphere

DOI10.3934/jmd.2015.9.141zbMath1333.37093arXiv1503.09035OpenAlexW1686649101MaRDI QIDQ496249

Kai Zehmisch, Gabriele Benedetti

Publication date: 21 September 2015

Published in: Journal of Modern Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.09035

zbMATH Keywords

periodic orbitscapacity boundsalmost existencemagnetic flowstwisted cotangent bundles over the two-sphere

Mathematics Subject Classification ID

Related Items (5)

On an integrable magnetic geodesic flow on the two-torus ⋮ On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus ⋮ On geodesic flows with symmetries and closed magnetic geodesics on orbifolds ⋮ Periodic orbits in virtually contact structures ⋮ The Lusternik–Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hofer-Zehnder capacity of unit disk cotangent bundles and the loop product
• 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
• Symplectic topology of Mañé's critical values
• Hamiltonian dynamics on convex symplectic manifolds
• Periodic solutions of Kirchhoff equations for the free motion of a rigid body in a fluid and the extended Lyusternik-Shnirel'man-Morse theory. I
• Periodic solutions on hypersurfaces and a result by C. Viterbo
• New generalizations of Poincaré's geometric theorem
• Geometry on the group of Hamiltonian diffeomorphisms
• Isotopy of symplectic balls, Gromov's radius and the structure of ruled symplectic 4-manifolds
• Hofer-Zehnder capacity and length minimizing Hamiltonian paths
• Relative Hofer-Zehnder capacity and periodic orbits in twisted cotangent bundles
• Transversality in elliptic Morse theory for the symplectic action
• On the existence of three closed magnetic geodesics for subcritical energies
• Gromov-Witten invariants and pseudo symplectic capacities
• Applications of Hofer's geometry to Hamiltonian dynamics
• The Palais-Smale condition on contact type energy levels for convex Lagrangian systems
• WEINSTEIN CONJECTURE AND GW-INVARIANTS
• The Structure of Rational and Ruled Symplectic 4-Manifolds
• The Hamiltonian formalism and a many-valued analogue of Morse theory
• The weinstein conjecture in the presence of holomorphic spheres
• THE WEINSTEIN CONJECTURE ON SOME SYMPLECTIC MANIFOLDS CONTAINING THE HOLOMORPHIC SPHERES
• A.D. Alexandrov spaces with curvature bounded below
• HOFER–ZEHNDER CAPACITY AND HAMILTONIAN CIRCLE ACTIONS
• A REFINEMENT OF THE HOFER–ZEHNDER THEOREM ON THE EXISTENCE OF CLOSED CHARACTERISTICS NEAR A HYPERSURFACE
• Existence of periodic solutions of Hamiltonian systems on almost every energy surface

This page was built for publication: On the existence of periodic orbits for magnetic systems on the two-sphere