Finite energy foliations of tight three-spheres and Hamiltonian dynamics

摘要: Surfaces of sections are a classical tool in the study 3-dimensional dynamical systems. Their use goes back to work Poincare and Birkhoff. In present paper we give natural generalization this concept by constructing system transversal complement finitely many distinguished periodic solutions. Such is established for nondegenerate Reeb flows on tight 3-sphere means pseudoholomorphic curves. The applications cover geodesic T1S2 - RP3 via its double covering S3, also Hamiltonian systems IR4 restricted sphere-like energy surfaces contact type.