Geometry and topology
Title: On the three-body problem, cone structures, entropy and open books.
Abstract: In this talk, I will describe how cone structures naturally appear in the context of Reeb flows adapted to iterated planar open books on contact 5-folds. I will also discuss a notion of topological entropy for cone structures on an arbitrary manifold with a metric, and discuss possible applications. In particular, I will outline how we expect to use this to prove that the dynamics of the spatial circular restricted three-body problem, in low energies and near the primaries, can be arbitrarily C^\infty-approximated by flows with positive topological entropy, whenever the planar problem is dynamicaly convex
This is work in progress with Umberto Hrnyewicz.