Non-resonant circles for strong magnetic fields on surfaces
Copyright policy )Non-resonant circles for strong magnetic fields on surfaces
We study non-resonant circles for strong magnetic fields on a closed, connected, oriented surface and show how these can be used to prove the existence of trapping regions and of periodic magnetic geodesics with prescribed low speed. As a corollary, there exist infinitely many periodic magnetic geodesics for every low speed in the following cases: i) the surface is not the two-sphere, ii) the magnetic field vanishes somewhere.
- Vrije Universiteit Amsterdam Netherlands
- International School for Advanced Studies Italy
Periodic and quasi-periodic flows and diffeomorphisms, Dynamical Systems (math.DS), Geodesics in global differential geometry, Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.), periodic orbits, Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, Flows on surfaces, magnetic systems, Mathematics - Symplectic Geometry, Magnetic systems, FOS: Mathematics, Periodic orbits of vector fields and flows, KAM tori, trapping regions, Symplectic Geometry (math.SG), Mathematics - Dynamical Systems, Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems, Variational problems in applications to the theory of geodesics (problems in one independent variable)
Periodic and quasi-periodic flows and diffeomorphisms, Dynamical Systems (math.DS), Geodesics in global differential geometry, Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.), periodic orbits, Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, Flows on surfaces, magnetic systems, Mathematics - Symplectic Geometry, Magnetic systems, FOS: Mathematics, Periodic orbits of vector fields and flows, KAM tori, trapping regions, Symplectic Geometry (math.SG), Mathematics - Dynamical Systems, Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems, Variational problems in applications to the theory of geodesics (problems in one independent variable)
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