Existence and localization of closed magnetic geodesics with low energy

Abstract: Magnetic flows are generalizations of geodesic flows that describe the motion of a charged particle in a magnetic field. While every closed Riemannian manifold admits at least one closed geodesic, the analogous problem for magnetic orbits (also known as magnetic geodesics) is significantly more challenging and has received considerable attention in recent decades. I will present a result establishing that every low energy level of any magnetic flow admits at least one contractible closed orbit, assuming only that the magnetic strength is not identically zero, has a compact strict local maximum K, and that the cohomology class of the magnetic field is spherically rational. Moreover, this magnetic geodesic can be localized within an arbitrarily small neighborhood of K. This is joint work with Valerio Assenza and Gabriele Benedetti.

algebraic geometrydifferential geometrysymplectic geometry

Audience: researchers in the topic

Geometria em Lisboa (IST)

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