Invariant foliations of non-degenerate bi-Hamiltonian structures

TL;DR

This paper characterizes all invariant distributions of non-degenerate bi-Hamiltonian structures and studies their local integrability near generic points.

Contribution

It provides a complete description of invariant distributions and analyzes their integrability in the context of bi-Hamiltonian geometry.

Findings

All invariant distributions are classified for non-degenerate bi-Hamiltonian structures.

Conditions for local integrability of these distributions are established.

The results enhance understanding of the geometric structure of bi-Hamiltonian systems.

Abstract

In this paper, we describe all invariant distributions of non-degenerate bi-Hamiltonian structures and investigate their integrability in the neighbourhood of a generic point.