39 citations · 140 across the 18 of their papers we have counts for
26 papers
Avoidance of non-strict saddle points by blow-up
El Mehdi Achour, Umberto L. Hryniewicz, Michael Westdickenberg
It is an old idea to use gradient flows or time-discretized variants thereof as methods for solving minimization problems. In some applications, for example in machine learning con…
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…
Generic properties of -dimensional Reeb flows: Birkhoff sections and entropy
Vincent Colin, Pierre Dehornoy, Umberto Hryniewicz +1
In this paper we use broken book decompositions to study Reeb flows on closed -manifolds. We show that if the Liouville measure of a nondegenerate contact form can be approximat…
Quantitative conditions for right-handedness of flows
Anna Florio, Umberto Hryniewicz
We give a numerical condition for right-handedness of a dynamically convex Reeb flow on the -sphere. Our condition is stated in terms of an asymptotic ratio between the amount o…
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…
Genus zero global surfaces of section for Reeb flows and a result of Birkhoff
Umberto L. Hryniewicz, Pedro A. S. Salomão, Krzysztof Wysocki
We exhibit sufficient conditions for a finite collection of periodic orbits of a Reeb flow on a closed -manifold to bound a positive global surface of section with genus zero. T…
A note on Schwartzman-Fried-Sullivan Theory, with an application
Umberto L. Hryniewicz
We prove a theorem on the existence of global surfaces of section with prescribed spanning orbits and homology class. This result is a modification and a refinement of a result due…
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…
A systolic inequality for geodesic flows on the two-sphere
Alberto Abbondandolo, Barney Bramham, Umberto L. Hryniewicz +1
For a Riemannian metric on the two-sphere, let be the length of the shortest closed geodesic and be the length of the longest simple closed ge…
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…
A Poincaré-Birkhoff theorem for tight Reeb flows on
Umberto Hryniewicz, Al Momin, Pedro A. S. Salomão
We consider Reeb flows on the tight -sphere admitting a pair of closed orbits forming a Hopf link. If the rotation numbers associated to the transverse linearized dynamics at th…
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…