Minimizing entropy for translation surfaces
Abstract
In this note, we consider the entropy of unit area translation surfaces in the $SL(2, \mathbb R)$ orbits of square tiled surfaces that are the union of squares, where the singularities occur at the vertices and the singularities have a common cone angle. We show that the entropy over such orbits is minimized at those surfaces tiled by equilateral triangles where the singularities occur precisely at the vertices.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.07929
 Bibcode:
 2021arXiv211007929C
 Keywords:

 Mathematics  Dynamical Systems
 EPrint:
 10 pages, 7 figures, typos corrected, Example 1.2 corrected