Related papers: Reeb orbits trapped by Denjoy minimal sets

We study the existence of multiple closed Reeb orbits on some contact manifolds by means of $S^1$-equivariant symplectic homology and the index iteration formula. It is proved that a certain class of contact manifolds which admit…

We give a sharp lower bound for the number of geometrically distinct contractible periodic orbits of dynamically convex Reeb flows on prequantizations of symplectic manifolds that are not aspherical. Several consequences of this result are…

We show that a nondegenerate tight contact form on the 3-sphere has exactly two simple closed Reeb orbits if and only if the differential in linearized contact homology vanishes. Moreover, in this case the Floquet multipliers and…

We prove a $C^\infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces. This is a consequence of a $C^\infty$ closing lemma for Reeb flows on closed contact three-manifolds, which was recently proved as an application of…

A $(2k+1)-$dimensional Lie algebra is called contact if it admits a one-form $\varphi$ such that $\varphi\wedge(d\varphi)^k\neq 0.$ Here, we extend recent work to describe a combinatorial procedure for generating contact, type-A Lie poset…

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…

We use the Boothby-Wang fibration to construct certain simply connected K-contact manifolds and we give sufficient and necessary conditions on when such K-contact manifolds are homeomorphic to the odd dimensional spheres. If the symplectic…

We prove that, for a $C^\infty$-generic contact form $\lambda$ adapted to a given contact distribution on a closed three-manifold, there exists a sequence of periodic Reeb orbits which is equidistributed with respect to $d\lambda$. This is…

We show that the differential in positive equivariant symplectic homology or linearized contact homology vanishes for non-degenerate Reeb flows with a continuous invariant Lagrangian subbundle (e.g. Anosov Reeb flows). Several applications…

Let $(M, \xi)$ be a compact contact 3-manifold and assume that there exists a contact form $\alpha_0$ on $(M, \xi)$ whose Reeb flow is Anosov. We show this implies that every Reeb flow on $(M, \xi)$ has positive topological entropy. Our…

In this paper, we prove that there exists a residual subset of contact forms $\lambda$ (if any) on a compact connected orientable manifold $M$ for which the foliation de Rham cohomology of the associated Reeb foliation $F_\lambda$ is…

A translated point of a contactomorphism $\phi$ on a contact manifold with contact form $\alpha$ is a point $p$ where $\alpha$ is preserved under $\phi$ and whose image under $\phi$ lies in the same Reeb trajectory. They were introduced as…

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…

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…

The first two authors showed in~\cite{AM1} how the Conley-Zehnder index of any contractible periodic Reeb orbit of a non-degenerate toric contact form on a good toric contact manifold with zero first Chern class, i.e. a Gorenstein toric…

Let $M$ be a connected compact contact toric manifold. Most of such manifolds are of Reeb type. We show that if $M$ is of Reeb type, then $\pi_1(M)$ is finite cyclic, and we describe how to obtain the order of $\pi_1(M)$ from the moment map…

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…

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…

Let $(Y,\lambda)$ be a non-degenerate contact three manifold. D. Cristfaro-Gardiner, M. Hutshings and D. Pomerleano showed that if $c_{1}(\xi=\mathrm{Ker}\lambda)$ is torsion, then the Reeb vector field of $(Y,\lambda)$ has infinity many…

Let $\Sigma$ be a connected closed three-manifold, and let $t_\Sigma$ be the order of the torsion subgroup of $H_1(\Sigma;\mathbb Z)$. For a contact form $\alpha$ on $\Sigma$, we denote by $\mathrm{Volume}(\alpha)$ the contact volume of…