English

Periodic orbits in virtually contact structures

Symplectic Geometry 2020-08-17 v4 Dynamical Systems

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 Ma\~n\'e 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.

Keywords

Cite

@article{arxiv.1705.02208,
  title  = {Periodic orbits in virtually contact structures},
  author = {Youngjin Bae and Kevin Wiegand and Kai Zehmisch},
  journal= {arXiv preprint arXiv:1705.02208},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-22T19:38:13.385Z