Classifying Linear Canonical Relations

Abstract

In this Master's thesis, we consider the problem of classifying, up to conjugation by linear symplectomorphisms, linear canonical relations (lagrangian correspondences) from a finite-dimensional symplectic vector space to itself. We give an elementary introduction to the theory of linear canonical relations and present partial results toward the classification problem. This exposition should be accessible to undergraduate students with a basic familiarity with linear algebra.

46 pages, 4 figures

References in corpus (1)

• (Co)isotropic Pairs in Poisson and Presymplectic Vector Spaces

Cited by in corpus (2)

• (Co)isotropic Pairs in Poisson and Presymplectic Vector Spaces
• On an Extension of the Mean Index to a large subset of Linear Canonical Relations