When different norms lead to same billiard trajectories?

TL;DR

This paper explores conditions under which different non-symmetric norms produce identical billiard reflection laws, extending previous research in the mathematical theory of billiards.

Contribution

It establishes new conditions for when two distinct non-symmetric norms lead to the same billiard reflection behavior, expanding understanding of billiard dynamics.

Findings

Identifies specific conditions for norm equivalence in billiard reflections

Extends previous work on symmetric norms to non-symmetric cases

Provides a framework for comparing billiard trajectories under different norms

Abstract

In this paper, extending the works of Milena Radnovi\'c and Serge Tabachnikov, we establish conditions for two different non-symmetric norms to define the same billiard reflection law.