Periodic Points of Ward-Veech Surfaces

TL;DR

This paper computes new examples of periodic points on non-arithmetic Veech surfaces, exploring their structure and applications to surface bundle classifications and Veech group properties.

Contribution

It provides explicit examples of periodic point sets for a family of non-hyperelliptic Veech surfaces with unbounded complexity, expanding understanding of their dynamics.

Findings

New periodic point sets computed for specific Veech surfaces

Applications to classifying holomorphic sections of surface bundles

Insights into the structure of infinitely generated Veech groups

Abstract

For a non-arithmetic Veech surface, it is known that the set points having finite orbit under the Veech group, called the set of periodic points, is finite. However, few examples of these periodic point sets have been computed. In what follows, we compute new examples of periodic point sets for a family of non-hyperelliptic Veech surfaces with unbounded complexity and consider applications to classifying the holomorphic sections of certain surface bundles as well as applications to the study of infinitely generated Veech groups.