2008/02/07 by John Smillie, Smillie, John, Barak Weiss +1
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS
paper · pdf · doi:10.48550/arxiv.0802.0919
arxiv created 2008/02/07 · openalex publication_date 2008/02/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For fixed g and T we show that finiteness of the set of affine equivalence classes of flat surfaces of genus g whose Veech groups contain a cusp of hyperbolic co-area less than T. We obtain new restrictions on Veech groups: we show that any non-elementary Veech group can appear only finitely many times in a fixed stratum, that any non-elementary Veech group is of finite index in its normalizer, and that the quotient of the upper half plane by a non-lattice Veech group contains arbitrarily large embedded disks. These are proved using the finiteness of the set of affine equivalence classes of flat surfaces of genus g whose Veech group contains a hyperbolic element with eigenvalue less than T.