Related papers: From one Reeb orbit to two
We establish the existence of a secondary Reeb orbit set with quantitative action and linking bounds for any contact form on the standard tight three-sphere admitting the standard transverse positive $T(p,q)$ torus knot as an elliptic Reeb…
We establish multiplicity results for geometrically distinct contractible closed Reeb orbits of non-degenerate contact forms on a broad class of prequantization bundles. The results hold under certain index requirements on the contact form…
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…
It is a conjecture of Colin and Honda that the number of Reeb periodic orbits of universally tight contact structures on hyperbolic manifolds grows exponentially with the period, and they speculate further that the growth rate of contact…
It's known from from work of Hofer, Wysocki, and Zehnder [1996] and Bourgeois [2002] that in a contact manifold equipped with either a nondegenerate or Morse-Bott contact form, a finite-energy pseudoholomorphic curve will be asymptotic at…
In this paper, we prove (1): for any closed contact three-manifold with a $C^\infty$-generic contact form, the union of periodic Reeb orbits is dense, (2): for any closed surface with a $C^\infty$-generic Riemannian metric, the union of…
In this short note, we prove that singular Reeb vector fields associated with generic $b$-contact forms have either (at least) $2N$ or an infinite number of escape orbits, where $N$ denotes the number of connected components of the critical…
Given two closed contact three-manifolds, one can form their contact connected sum via the Weinstein one-handle attachment. We study how pseudo-holomorphic curves in the symplectization behave under this operation. As a result, we give a…
We prove the existence of an elliptic Reeb orbit for some contact forms on the real projective three space $\mathbb{R} P^3$. The main ingredient of the proof is the existence of a distinguished pseudoholomorphic curve in the symplectization…
In this article, we investigate Reeb dynamics on $b^m$-contact manifolds, previously introduced in [MiO], which are contact away from a hypersurface $Z$ but satisfy certain transversality conditions on $Z$. The study of these contact…
An important class of contact 3--manifolds are those that arise as links of rational surface singularities with reduced fundamental cycle. We explicitly describe symplectic caps (concave fillings) of such contact 3--manifolds. As an…
In this note, we consider contractible loops of contactomorphisms that are positive over some non-empty closed subset of a contact manifold. Such closed subsets are called immaterial. We argue that the complement of a Reeb-invariant…
We investigate the effect of a hyperbolic (or, more generally, isolated as an invariant set) closed Reeb orbit on the dynamics of a Reeb flow on the $(2n-1)$-dimensional standard contact sphere, extending two results previously known for…
In this paper we prove two isomorphisms in the local symplectic homology of a simple, which is to say non iterated, isolated Reeb orbit. The isomorphisms are in $S^1$-equivariant and nonequivariant symplectic homology, relating the local…
In this note we show that a closed oriented contact manifold is obtained from the standard contact sphere of the same dimension by contact surgeries on isotropic and coisotropic spheres. In addition, we observe that all closed oriented…
We prove that every smooth closed manifold admits a smooth real-valued function with only two critical values. We call a function of this type a \emph{Reeb function}. We prove that for a Reeb function we can prescribe the set of minima (or…
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…
If $\eta$ is a contact form on a manifold $M$ such that the orbits of the Reeb vector field form a simple foliation $\mathcal{F}$ on $M$, then the presymplectic 2-form $d\eta$ on $M$ induces a symplectic structure $\omega$ on the quotient…
The aim of the paper is three-fold. We begin by proving a formula, both global and local versions, relating the number of periodic orbits of an iterated map and the Lefschetz numbers, or indices in the local case, of its iterations. This…
The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces. More precisely, we will show that (1) if $(M,\omega)$ admits a…