# Cyclic hyperbolic Veech groups in finite area

## TL;DR

This paper demonstrates the existence of finite area flat surfaces whose Veech groups are infinite cyclic groups generated solely by hyperbolic elements, expanding understanding of Veech group structures.

## Contribution

It proves the existence of finite area flat surfaces with Veech groups that are infinite cyclic groups generated by hyperbolic elements, a novel structural insight.

## Key findings

- Existence of finite area flat surfaces with cyclic hyperbolic Veech groups
- Veech groups can be infinite cyclic and hyperbolic
- Advances understanding of Veech group classifications

## Abstract

We prove that there are finite area flat surfaces whose Veech group is an infinite cyclic group consisting of hyperbolic elements