Topological entropy for reeb vector fields in dimension three via open book decompositions

Marcelo R R Alves (1) , Vincent Colin (2) , Ko Honda (3)

1 UNINE - Université de Neuchâtel = University of Neuchatel
2 UN - Université de Nantes
3 UCLA - University of California [Los Angeles]

Given an open book decomposition of a contact three man-ifold (M, ξ) with pseudo-Anosov monodromy and fractional Dehn twist coefficient c = k n , we construct a Legendrian knot Λ close to the stable foliation of a page, together with a small Legendrian pushoff Λ. When k ≥ 5, we apply the techniques of [CH2] to show that the strip Legen-drian contact homology of Λ → Λ is well-defined and has an exponential growth property. The work [Al2] then implies that all Reeb vector fields for ξ have positive topological entropy.

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

Marcelo R R Alves, Vincent Colin, Ko Honda. Topological entropy for reeb vector fields in dimension three via open book decompositions. 2017. ⟨hal-01525793v1⟩