Genericity of Caustics on a corner

TL;DR

This paper introduces new equivalence relations for reticular Lagrangian maps to classify generic caustics on corners in 2D and 3D manifolds, providing a comprehensive geometric framework.

Contribution

It proposes the concepts of caustic-equivalence and weak caustic-equivalence for reticular Lagrangian maps, enabling a systematic classification of caustics on corners.

Findings

All generic caustics on a corner in 2D and 3D are characterized.

Figures illustrating all types of generic caustics are provided.

The classification framework is based on the introduced equivalence relations.

Abstract

We introduce the notions of the caustic-equivalence and the weak caustic-equivalence relations of reticular Lagrangian maps in order to give a generic classification of caustics on a corner. We give the figures of all generic caustics on a corner in a smooth manifold of dimension 2 and 3.