Semi-global symplectic invariants

Holger Dullin
Dept. of Mathematics, Loughborough University

Consider the contourplots of two distinct functions of two variables. Let there be critical saddle points in both of them, and consider them together with their separatrices. Under what conditions can we find an area preserving map from a neighbourhood of the separatrix of the first contourplot to that of the second contourplot preserving contourlines? This question can be answered by introducing symplectic invariants of a saddle point with its separatrix. The construction and explanation of these invariants is the purpose of this talk.