First occurring singularities of functions on symplectic semi-space

K. Kourliouros, M. Zhitomirski

Abstract

We explain how the classical theorem by Arnol’d and Melrouse on non-singular functions on a symplectic manifold with a boundary can be proved in few lines, and we use the same method to obtain a new result, which is a normal forms with functional invariants for the first occurring singularities.