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 on three dimensional manifolds with compact embedded critical surfaces have either (at least) 2N or an infinite number of escape orbits, where N denotes the number of connected components of the critical set. In case where the first Betti number of a connected component of the critical surface is positive, there exist infinitely many escape orbits. A similar result holds in the case of b -Beltrami vector fields that are not b -Reeb. The proof is based on a more detailed analysis of the main result in [19]. © 2023, Pleiades Publishing, Ltd.