2015/05/11 by Hryniewicz, Umberto L., Salomão, Pedro A. S. · 1 citation
#53D42 #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1505.02713
The first result of this paper is that every contact form on ℝ P3 sufficiently C^∞-close to a dynamically convex contact form admits an elliptic-parabolic closed Reeb orbit which is 2-unknotted, has self-linking number -1/2 and transverse rotation number in (1/2,1]. Our second result implies that any p-unknotted periodic orbit with self-linking number -1/p of a dynamically convex Reeb flow on a lens space of order p is the binding of a rational open book decomposition, whose pages are global surfaces of section. As an application we show that in the planar circular restricted three-body problem for energies below the first Lagrange value and large mass ratio, there is a special link consisting of two periodic trajectories for the massless satellite near the smaller primary -- lunar problem -- with the same contact-topological and dynamical properties of the orbits found by Conley in~\citeconley for large negative energies. Both periodic trajectories bind rational open book decompositions with disk-like pages which are global surfaces of section. In particular, one of the components is an elliptic-parabolic periodic orbit.