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Reeb orbits frequently intersecting a symplectic surface
Michael Hutchings
Consider a symplectic surface in a three-dimensional contact manifold with boundary on Reeb orbits (periodic orbits of the Reeb vector field). We assume that the rotation numbers o…
Anchored symplectic embeddings
Michael Hutchings, Agniva Roy, Morgan Weiler +1
Given two four-dimensional symplectic manifolds, together with knots in their boundaries, we define an ``anchored symplectic embedding'' to be a symplectic embedding, together with…
Zeta functions of dynamically tame Liouville domains
Michael Hutchings
We define a dynamical zeta function for nondegenerate Liouville domains, in terms of Reeb dynamics on the boundary. We use filtered equivariant symplectic homology to (i) extend th…
Hopf orbits and the first ECH capacity
Umberto Hryniewicz, Michael Hutchings, Vinicius G. B. Ramos
We consider dynamically convex star-shaped domains in a symplectic vector space of dimension . For such a domain, a ``Hopf orbit'' is a closed characteristic in the boundary whi…
Proof of Hofer-Wysocki-Zehnder's two or infinity conjecture
Dan Cristofaro-Gardiner, Umberto Hryniewicz, Michael Hutchings +1
We prove that every Reeb flow on a closed connected three-manifold has either two or infinitely many simple periodic orbits, assuming that the associated contact structure has tors…