Structures bihamiltoniennes partielles

TL;DR

This paper introduces three new notions of partial bihamiltonian structures within a modern geometric framework, exploring their properties and providing examples in both finite and infinite-dimensional contexts.

Contribution

It defines and studies three types of partial bihamiltonian structures in a general geometric setting, expanding the understanding of their properties and applications.

Findings

Introduction of three partial bihamiltonian structures (PQ, PN, PΩ).

Analysis of geometric objects associated with these structures.

Examples provided in finite and infinite-dimensional spaces.

Abstract

We introduce three notions of partial bihamiltonian structures ($\operatorname{PQ}$, $\operatorname{PN}$ et $\operatorname{P\Omega}$) in the convenient setting defined by Fr\"{o}licher, Kriegl and Michor. We study geometrical objects linked with these structures and give examples in finite and infinite dimensions.