arXiv subjects

Andres Perico

Publications and source records attributed to Andres Perico.

2 recordsLinked to original sources

arXiv2020

Inverse-Magnetic Billiards on a Square

We consider a polygon in a two-dimensional plane with a homogeneous constant magnetic field orthogonal to such plane, but inside the polygon, the magnetic field is zero. We study the dynamics of an electron with an initial velocity in this setting. Problems arise because we have a boundary with corners. In the square case, we generalize velocities with a rational slope and show numerical evidence of a chaotic-like behavior with other initial conditions.

math.DS↗

arXiv2018

Sard's conjecture for degenerate Engel

Let D be a rank 2 bracket generating distribution on a 4 manifold, D is Engel if its growth vector is maximal. When this maximality fails the distribution is degenerate. We prove Sard's conjecture for the endpoint map in the case of degenerate Engel distributions. In this case the set of singular horizontal curves starting from the same point has measure zero: a full 2 dimensional disk.

math.DS↗