39 citations · 140 across the 18 of their papers we have counts for
19 papers · 1 filter
On the knot types of periodic Reeb orbits of dynamically convex contact forms
Umberto L. Hryniewicz, Pedro A. S. Salomão, Richard Siefring
We exhibit transverse knot types on the standard contact -sphere that cannot be realized as periodic Reeb orbits of a dynamically convex contact form. In particular, such transv…
Homoclinic orbits, Reeb chords and nice Birkhoff sections for Reeb flows in 3D
Vincent Colin, Umberto Hryniewicz, Ana Rechtman
We prove that for a -generic contact form defining a given co-oriented contact structure on a closed -manifold, every hyperbolic periodic Reeb orbit admits a transvers…
Genus zero transverse foliations for weakly convex Reeb flows on the tight -sphere
Naiara V. de Paulo, Umberto Hryniewicz, Seongchan Kim +1
A contact form on the tight -sphere is called weakly convex if the Conley-Zehnder index of every Reeb orbit is at least . In this article, we study Reeb flows of…
Contact three-manifolds with exactly two simple Reeb orbits
Dan Cristofaro-Gardiner, Umberto Hryniewicz, Michael Hutchings +1
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 exactl…
Global surfaces of section with positive genus for dynamically convex Reeb flows
Umberto L. Hryniewicz, Pedro A. S. Salomão, Richard Siefring
We establish some new existence results for global surfaces of section of dynamically convex Reeb flows on the three-sphere. These sections often have genus, and are the result of…
On the relation between action and linking
David Bechara Senior, Umberto L. Hryniewicz, Pedro A. S. Salomão
We introduce numerical invariants of contact forms in dimension three and use asymptotic cycles to estimate them. As a consequence, we prove a version for Anosov Reeb flows of resu…
Sharp systolic inequalities for Riemannian and Finsler spheres of revolution
Alberto Abbondandolo, Barney Bramham, Umberto L. Hryniewicz +1
We prove that the systolic ratio of a sphere of revolution does not exceed and equals if and only if is Zoll. More generally, we consider the rotationally symmetric…
Global surfaces of section for Reeb flows in dimension three and beyond
Umberto L. Hryniewicz, Pedro A. S. Salomão
We survey some recent developments in the quest for global surfaces of section for Reeb flows in dimension three using methods from Symplectic Topology. We focus on applications to…
Systolic ratio, index of closed orbits and convexity for tight contact forms on the three-sphere
Alberto Abbondandolo, Barney Bramham, Umberto Hryniewicz +1
We construct a dynamically convex contact form on the three-sphere whose systolic ratio is arbitrarily close to 2. This example is related to a conjecture of Viterbo, whose validit…
Contact forms with large systolic ratio in dimension three
Alberto Abbondandolo, Barney Bramham, Umberto L. Hryniewicz +1
The systolic ratio of a contact form on a closed three-manifold is the quotient of the square of the shortest period of closed Reeb orbits by the contact volume. We show that every…
Transversality for local Morse homology with symmetries and applications
Doris Hein, Umberto L. Hryniewicz, Leonardo Macarini
We prove the transversality result necessary for defining local Morse chain complexes with finite cyclic group symmetry. Our arguments use special regularized distance functions co…
Elliptic bindings for dynamically convex Reeb flows on the real projective three-space
Umberto L. Hryniewicz, Pedro A. S. Salomão
The first result of this paper is that every contact form on sufficiently -close to a dynamically convex contact form admits an elliptic-parabolic closed…
Sharp systolic inequalities for Reeb flows on the three-sphere
A. Abbondandolo, B. Bramham, U. L. Hryniewicz +1
The systolic ratio of a contact form on the three-sphere is the quantity \[ ρ_{\mathrm{sys}}(α) = \frac{T_{\min}(α)^2}{\mathrm{vol}(S^3,α\wedge dα)}, \] where is…
Closed Reeb orbits on the sphere and symplectically degenerate maxima
Viktor L. Ginzburg, Doris Hein, Umberto L. Hryniewicz +1
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.…
Local contact homology and applications
Umberto Hryniewicz, Leonardo Macarini
We introduce a local version of contact homology for an isolated periodic orbit of the Reeb flow and prove that its rank is uniformly bounded for isolated iterations. Several appli…
Systems of global surfaces of section for dynamically convex Reeb flows on the 3-sphere
Umberto Hryniewicz
We characterize which closed Reeb orbits of a dynamically convex contact form on the 3-sphere bound disk-like global surfaces of section for the Reeb flow, without any genericity a…
Global properties of tight Reeb flows with applications to Finsler geodesic flows on
Umberto Hryniewicz, Pedro A. S. Salomão
We show that if a Finsler metric on with reversibility has flag curvatures satisfying , then closed geodesics with specific contact-topol…
On the existence of disk-like global sections for Reeb flows on the tight 3-sphere
Umberto Hryniewicz, Pedro A. S. Salomão
We consider Reeb dynamics on the 3-sphere associated to a tight contact form. Our main result gives necessary and sufficient conditions for a periodic Reeb orbit to bound a disk-li…
Fast finite-energy planes in symplectizations and applications
Umberto Hryniewicz
We define the notion of fast finite-energy planes in the symplectization of a closed 3-dimensional energy level of contact type. We use them to construct special open book deco…