Normal forms of Poisson structures near a symplectic leaf

TL;DR

This paper extends Vorobjev's formalism to establish general results on linearization and normal forms of Poisson structures near symplectic leaves, enhancing understanding of their local behavior.

Contribution

It provides new theoretical results on the normal form and linearization of Poisson structures around symplectic leaves using Vorobjev's formalism.

Findings

General results on Poisson structure linearization near symplectic leaves

Enhanced understanding of local Poisson geometry

Framework for normal form classification

Abstract

We show how one can handle the formalism developped by Yurii Vorobjev in order to give general results about the problems of linearisation and of normal form of a Poisson structure in the neighborhood of one of its symplectic leaves.