Periodic orbits in virtually contact structures

Abstract

We prove that certain non-exact magnetic Hamiltonian systems on products of closed hyperbolic surfaces and with a potential function of large oscillation admit non-constant contractible periodic solutions of energy below the Mañé critical value. For that we develop a theory of holomorphic curves in symplectizations of non-compact contact manifolds that arise as the covering space of a virtually contact structure whose contact form is bounded with all derivatives up to order three.

Theorem 1.1 added, version accepted for publication in J. Topol. Anal, typos corrected

References in corpus (4)

• The multiplicity problem for periodic orbits of magnetic flows on the 2-sphere
• On the existence of periodic orbits for magnetic systems on the two-sphere
• Finsler geodesics, periodic Reeb orbits, and open books
• Two constructions of virtually contact structures

Cited by in corpus (3)

• Symplectic dynamics of contact isotropic torus complements
• Two constructions of virtually contact structures
• The singular Weinstein conjecture