Automorphisms of Quadratic Liouville Structures

TL;DR

This paper characterizes the symplectomorphisms of a symplectic vector space that preserve specific quadratic Liouville structures, providing explicit descriptions for certain classes of potentials.

Contribution

It offers an explicit classification of automorphisms preserving quadratic Liouville structures differing from the canonical potential by a quadratic differential.

Findings

Explicit descriptions of automorphisms for three classes of quadratic potentials

Classification of diffeomorphisms preserving these structures

Extension of known symplectic automorphism results

Abstract

We examine the diffeomorphisms of a symplectic vector space that preserve a chosen symplectic potential. Our examination yields an explicit description of these diffeomorphisms when the chosen potential differs from the canonical potential by the differential of a homogeneous quadratic in one of three broad classes.