Related papers: Reeb periodic orbits after a bypass attachment

A contact manifold admittting a supporting contact form without contractible Reeb orbits is called hypertight. In this paper we construct a Rabinowitz Floer homology associated to an arbitrary supporting contact form for a hypertight…

As a generalisation of the periodic orbit structure often seen in reflection or mirror symmetric MHD equilibria, we consider equilibria with other orientation-reversing symmetries. An example of such a symmetry, which is a not a reflection,…

We use the equivalence between embedded contact homology and Seiberg-Witten Floer homology to obtain the following improvements on the Weinstein conjecture. Let Y be a closed oriented connected 3-manifold with a stable Hamiltonian…

A regular contact manifold is a manifold $M$ equipped with a globally defined contact form $\eta$ such that the topological space $M/\mathcal{R}$ of orbits (trajectories) of the Reeb vector field $\mathcal{R}$ of $\eta$ carries a smooth…

This paper investigates the global structures of periodic orbits that appear in Rayleigh-B\'enard convection, which is modeled by a two-dimensional perturbed Hamiltonian model, by focusing upon resonance, symmetry and bifurcation of the…

Through the use of sub-Riemannian metrics we provide quantitative estimates for the maximal tight neighbourhood of a Reeb orbit on a three-dimensional contact manifold. Under appropriate geometric conditions we show how to construct closed…

We survey various recent results on the existence and properties of periodic orbits of Reeb vector fields in three dimensions. We give an introduction to the "elementary spectral invariants" of contact three-manifolds, and we explain how…

A topological mating is a map defined by gluing together the filled Julia sets of two quadratic polynomials. The identifications are visualized and understood by pinching ray-equivalence classes of the formal mating. For postcritically…

Let Q be a Riemannian manifold such that the Betti numbers of its free loop space with respect to some coefficient field are unbounded. We show that every contact form on its unit contangent bundle supporting the natural contact structure…

In this paper we deal with the existence of periodic orbits of geodesible vector fields on closed 3-manifolds. A vector field is geodesible if there exists a Riemannian metric on the ambient manifold making its orbits geodesics. In…

In this article, we first give a proof on the Arnold chord conjecture which states that every Reeb flow has at least as many Reeb chords as a smooth function on the Legendre submanifold has critical points on contact manifold. Second, we…

We introduce a new operad-like structure that we call a reconnectad; the ``input'' of an element of a reconnectad is a finite simple graph, rather than a finite set, and ``compositions'' of elements are performed according to the notion of…

A Reeb vector field satisfies the Kupka-Smale condition when all its closed orbits are non-degenerate, and the stable and unstable manifolds of its hyperbolic closed orbits intersect transversely. We show that, on a closed 3-manifold, any…

Two-dimensional electron dispersions with peculiar band crossings provide a platform for realizing topological phases of matter. Here we theoretically show that the $e_g$-orbital manifold of honeycomb-layered transition metal compounds…

A contact form on the tight $3$-sphere $(S^3,\xi_0)$ is called weakly convex if the Conley-Zehnder index of every Reeb orbit is at least $2$. In this article, we study Reeb flows of weakly convex contact forms on $(S^3,\xi_0)$ admitting a…

In this paper we use broken book decompositions to study Reeb flows on closed $3$-manifolds. We show that if the Liouville measure of a nondegenerate contact form can be approximated by periodic orbits, then there is a Birkhoff section for…

We apply the method of filling with holomorphic discs to a 4-dimensional symplectic cobordism with the standard contact 3-sphere as a convex boundary component. We establish the following dichotomy: either the cobordism is diffeomorphic to…

Let A be an affine variety inside a complex N dimensional vector space which has an isolated singularity at the origin. The intersection of A with a very small sphere turns out to be a contact manifold called the link of A. Any contact…

We show that the existence of one simple closed Reeb orbit of a particular type (a symplectically degenerate maximum) forces the Reeb flow to have infinitely many periodic orbits. We use this result to give a different proof of a recent…

In this paper we prove the existence of infinitely many closed Reeb orbits for a certain class of contact manifolds. This result can be viewed as a contact analogue of the Hamiltonian Conley conjecture. The manifolds for which the contact…