Study on Numerical Models & Symplectic Manifolds for Integral Equations

Exploring the Connection between Numerical Symplectic Geometry and Singularity Theory

Abstract

A symplectic two m-dimensional manifoldor bifold(Ő)represented by a closed form τwhere, τmdiminishes transversally as well as τ is confined maximally non-degenerate hyper methods H. This H is also known as folding hyper-methods. This is the way of introducing folded-symplectic form which is nothing but the conjunction of more than one symplectic manifolds. A Numerical, folded symplectic or bifold can be said a folded-symplectic manifold (Ő2m, τ) equipped with an effective, Hamiltonian action of a torus (T) with dimension m. This whole complex system is nothing but the generalizations of Numerical as well as symplectic or bifolds with deep sense of hypermethodss.The Analysis of these symplectic orbifolds is a connection among Numerical symplectic geometry singularity theory. The aim of these two is complementary to each other as one provide smooth functioning to degenerate while other’s degeneracies are far away.