# Golden ratio on nonorientable surfaces

## TL;DR

This paper demonstrates that on nonorientable surfaces of odd genus at least 5, there exist mapping classes with invariant subsurfaces exhibiting the golden ratio as their dilatation.

## Contribution

It introduces specific mapping classes on nonorientable surfaces that have the golden ratio as their dilatation, expanding understanding of surface dynamics.

## Key findings

- Existence of mapping classes with golden ratio dilatation on nonorientable surfaces
- Construction of invariant subsurfaces with golden ratio dilatation
- Applicable to surfaces of odd genus g ≥ 5

## Abstract

On each nonorientable surface of odd genus $g \geq 5$, we give a mapping class whose dilatation on an invariant subsurface is the golden ratio.