TOPOLOGICAL ENTROPY FOR REEB VECTOR FIELDS IN DIMENSION THREE VIA OPEN BOOK DECOMPOSITIONS

Marcelo R R Alves (1) , Vincent Colin (2, 3) , Ko Honda (4)

1 UNINE - Université de Neuchâtel = University of Neuchatel
2 UN - Université de Nantes
3 LMJL - Laboratoire de Mathématiques Jean Leray
4 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. Journal de l'École polytechnique — Mathématiques, 2019, 6, pp.119--148. ⟨hal-01525793v2⟩