Periodic points on the regular and double $n$-gon surfaces

TL;DR

This paper classifies periodic points on regular and double n-gon translation surfaces and explores implications for the finite blocking problem in rational triangles that unfold into these surfaces.

Contribution

It provides a complete classification of periodic points on these surfaces using the transfer principle, advancing understanding of their geometric and dynamical properties.

Findings

Classified all periodic points on regular and double n-gon surfaces.

Derived consequences for the finite blocking problem in rational triangles.

Enhanced understanding of translation surface dynamics.

Abstract

Using the transfer principle, we classify the periodic points on the regular $n$-gon and double $n$-gon translation surfaces and deduce consequences for the finite blocking problem on rational triangles that unfold to these surfaces.