Genericity of Caustics and Wavefronts on an r-corner

TL;DR

This paper classifies caustics and wavefronts generated by hypersurfaces with or without boundaries using reticular Lagrangian and Legendrian maps, providing a generic framework for understanding their structures.

Contribution

It introduces a generic classification scheme for caustics and wavefronts via reticular Lagrangian and Legendrian maps, extending understanding to hypersurfaces with boundaries.

Findings

Classification of caustics and wavefronts achieved

Reticular maps provide a unified framework

Results applicable to hypersurfaces with boundaries

Abstract

We investigate genericities of reticular Lagrangian maps and reticular Legendrian maps in order to give generic classifications of caustics and wavefronts generated by a hypersurface germ without or with a boundary in a smooth manifold.