39 citations · 140 across the 18 of their papers we have counts for
3 papers · 1 filter
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…