14 citations · 27 across the 16 of their papers we have counts for
19 papers
Left-handed geodesic flow of spheres of revolution
Pierre Dehornoy, Ana Rechtman
A flow on a 3-manifold is left-handed if any two ergodic invariant measures have negative linking number. We prove that on a 2-sphere of revolution whose curvature is -pinched…
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…
Properties of contact toric structures and concave boundaries of linear plumbings
Aleksandra Marinković, Jo Nelson, Ana Rechtman +3
We consider plumbings of symplectic disk bundles over spheres admitting concave contact boundary, with the goal of understanding the geometric properties of the boundary contact st…
Periodic orbits and Birkhoff sections of stable Hamiltonian structures
Robert Cardona, Ana Rechtman
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 define…
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…
Kuperberg Dreams
Steven Hurder, Ana Rechtman
The ``Seifert Conjecture'' stated, ``Every non-singular vector field on the 3-sphere has a periodic orbit''. In a celebrated work, Krystyna Kuperberg gave a constru…