ORBIT GROWTH OF CONTACT STRUCTURES AFTER SURGERY

Patrick Foulon (1) , Boris Hasselblatt (2) , Anne Vaugon (3)

1 CIRM - Centre International de Rencontres Mathématiques
2 Department of Mathematics, Tufts University
3 LMO - Laboratoire de Mathématiques d'Orsay

Investigation of the effects of a contact surgery construction and of invariance of contact homology reveals a rich new field of inquiry at the intersection of dynamical systems and contact geometry. We produce contact 3-flows not topologically orbit-equivalent to any algebraic flow, including examples on many hyperbolic 3-manifolds, and we show how the surgery produces dynamical complexity for any Reeb flow compatible with the resulting contact structure. This includes exponential complexity when neither the surg-ered flow nor the surgered manifold are hyperbolic. We also demonstrate the use in dynamics of contact homology, a powerful tool in contact geometry.

Mots clés: Anosov flow; 3-manifold; contact structure; Reeb flow; surgery; contact homology

Domaines: Systèmes dynamiques [math.DS]; Géométrie symplectique [math.SG]

Patrick Foulon, Boris Hasselblatt, Anne Vaugon. ORBIT GROWTH OF CONTACT STRUCTURES AFTER SURGERY. 2019. ⟨hal-02336690⟩