# Finsler perturbation with nondense geodesics with irrational directions

## TL;DR

This paper demonstrates that on flat Finsler tori, it is possible to create nondense geodesics with irrational directions through small smooth perturbations, highlighting intricate geodesic behaviors.

## Contribution

It introduces a method to produce nondense geodesics with irrational directions on Finsler tori via small smooth perturbations.

## Key findings

- Nondense geodesics can be generated with irrational directions.
- Small $C^{
abla}$-smooth perturbations suffice to alter geodesic density.
- The method applies to any Liouville direction on flat Finsler tori.

## Abstract

We show that given any Liouville direction and flat Finsler torus, one can make a $C^{\infty}$-small perturbation on an arbitrarily small disc to get a nondense geodesic in the given direction.