From 2N to infinitely many escape orbits

Abstract

In this short note, we prove that singular Reeb vector fields associated with generic $b$-contact forms have either (at least) $2N$ or an infinite number of escape orbits, where $N$ denotes the number of connected components of the critical set.

16 pages, for Alain Chenciner on his 2N-birthday. The article has undergone substantial improvement incorporating stronger results and introducing a novel count of escape orbits with multiplicity