On natural Poisson bivectors on the sphere

Abstract

We discuss the concept of natural Poisson bivectors, which allows us to consider the overwhelming majority of known integrable systems on the sphere in framework of bi-Hamiltonian geometry.

LaTeX with AMS fonts, 18 pages, version for the journal

References in corpus (4)

• Two-dimensional superintegrable metrics with one linear and one cubic integral
• On algebraic construction of certain integrable and super-integrable systems
• On bi-hamiltonian geometry of the Lagrange top
• A note on elliptic coordinates on the Lie algebra e(3)

Cited by in corpus (8)

• One invariant measure and different Poisson brackets for two nonholonomic systems
• On the Routh sphere problem
• Separation of variables for the generalized Henon-Heiles system and system with quartic potential
• Integrable systems on the sphere associated with genus three algebraic curves
• New Variables of Separation for the Steklov-Lyapunov System
• On one integrable system with a cubic first integral
• On a Trivial Family of Noncommutative Integrable Systems
• Deformations of the Poisson brackets and the Kowalevski top