Reeb vector fields and open book decompositions

We determine parts of the contact homology of certain contact 3-manifolds inthe framework of open book decompositions, due to Giroux. We study two cases:when the monodromy map of the compatible open book is periodic and when it ispseudo-Anosov. For an open book with periodic monodromy, we verify theWeinstein conjecture. In the case of an open book with pseudo-Anosov monodromy,suppose the boundary of a page of the open book is connected and the fractionalDehn twist coefficient $c={k\over n}$, where $n$ is the number of prongs alongthe boundary. If $k\geq 2$, then there is a well-defined linearized contacthomology group. If $k\geq 3$, then the linearized contact homology isexponentially growing with respect to the action, and every Reeb vector fieldof the corresponding contact structure admits an infinite number of simpleperiodic orbits.