Related papers: Reeb orbits frequently intersecting a symplectic s…

We study Reeb dynamics on the three-sphere equipped with a tight contact form and an anti-contact involution. We prove the existence of a symmetric periodic orbit and provide necessary and sufficient conditions for it to bound an invariant…

Stable Hamiltonian structures generalize contact forms and define a volume-preserving vector field known as the Reeb vector field. We study two aspects of Reeb vector fields defined by stable Hamiltonian structures on 3-manifolds: on one…

It is known that every contact form on a closed three-manifold has at least two simple Reeb orbits, and a generic contact form has infinitely many. We show that if there are exactly two simple Reeb orbits, then the contact form is…

We show that every (possibly degenerate) contact form on a closed three-manifold has at least two embedded Reeb orbits. We also show that if there are only finitely many embedded Reeb orbits, then their symplectic actions are not all…

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 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…

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…

A long standing conjecture in Hamiltonian Dynamics states that every contact form on the standard contact sphere $S^{2n+1}$ has at least $n+1$ simple periodic Reeb orbits. In this work, we consider a refinement of this problem when the…

We prove that for a $C^\infty$-generic contact form defining a given co-oriented contact structure on a closed $3$-manifold, every hyperbolic periodic Reeb orbit admits a transverse homoclinic connection in each of the branches of its…

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…

We characterise boundary shaped disc like neighbourhoods of certain isotropic submanifolds in terms of aperiodicity of Reeb flows. We prove uniqueness of homotopy and diffeomorphism type of such contact manifolds assuming non-existence of…

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…

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…

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 prove that there exists at least one close orbit in a given contact hypersurface in some symplectic manifolds.

A contact form is called K-contact if its Reeb vector field is Killing with respect to some Riemannian metric. In this paper we classify K-contact forms whose Reeb vector field admits at least one non-periodic orbit, on three-dimensional…

We exhibit transverse knot types on the standard contact $3$-sphere that cannot be realized as periodic Reeb orbits of a dynamically convex contact form. In particular, such transverse knot types do not arise as closed characteristics 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…

In this paper, it is proved that under dynamically convex condition, there exist at least $[\frac{n+1}{2}]$ closed Reeb orbits on a closed contact type hypersurface in $T^*S^n$ enclosing the zero section and bounding a simply connected…

We show that whenever a Hamiltonian diffeomorphism or a Reeb flow has a finite number of periodic orbits, the mean indices of these orbits must satisfy a resonance relation, provided that the ambient manifold meets some natural…