On the Finsler metrics obtained as limits of chessboard structures

TL;DR

This paper investigates the geodesic properties of a planar chessboard pattern with two values, and explores how these properties lead to Finsler metrics through homogenization of oscillating structures.

Contribution

It introduces a method to derive Finsler metrics as limits of oscillating chessboard structures, linking geometric properties to homogenization techniques.

Findings

Characterization of geodesics in chessboard structures

Derivation of Finsler metrics via homogenization

Insights into the limit behavior of oscillating patterns

Abstract

We study the geodesics in a planar chessboard structure with two values 1 and $\beta>1$. The results for a fixed structure allow us to infer the properties of the Finsler metrics obtained, with an homogenization procedure, as limit of oscillating chessboard structures.