Symmetric periodic orbits and invariant disk-like global surfaces of section on the three-sphere.

摘要: We study Reeb dynamics on the three-sphere equipped with a tight contact form and an anti-contact involution. prove existence of symmetric periodic orbit provide necessary sufficient conditions for it to bound invariant disk-like global surface section. also same questions under presence additional symmetry obtain similar results in this case. The proofs make use pseudoholomorphic curves symplectizations. As applications, we Birkhoff's conjecture surfaces section planar circular restricted three-body problem closed Finsler geodesics two-sphere. present applications some classical Hamiltonian systems.