An observation concerning uniquely ergodic vector fields on 3-manifolds

2008/11/24 by Clifford Henry Taubes, Taubes, Clifford Henry
Mathematics · #57R17 #57R57 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT #msc:57R17 #msc:57R57

paper · pdf · doi:10.48550/arxiv.0811.3983

arxiv created 2008/11/24 · arxiv updated 2009/12/01

Abstract

This paper proves the following: A volume preserving vector field on a compact 3-manifold whose dual 2-form is exact can not generate uniquely ergodic dynamics unless its asymptotic linking number is zero.

Related

• Asymptotic link invariants for ergodic vector fields
• A Remark on Unique Ergodicity and the Contact Type Condition
• Analytic uniquely ergodic volume preserving maps on odd spheres
• Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds
• Non-vanishing complex vector fields and the Euler characteristic