Analytic Extension of the Birkhoff Normal Forms for the Free Rigid Body Dynamics on SO(3)

2013/07/20 by Jean–Pierre Françoise, Francoise, Jean-Pierre, Daisuke Tarama +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1307.5412

openalex publication_date 2013/07/20 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Birkhoff normal form is a power series expansion associated with the local behavior of the Hamiltonian systems near a critical point. It is known to be convergent for integrable systems under some non-degeneracy conditions. By means of an expression of the inverse of Birkhoff normal form by a period integral, analytic continuation of the Birkhoff normal forms is considered for the free rigid body dynamics on SO(3). The global behavior of the Birkhoff normal forms is clarified in relation to the monodromy of an elliptic fibration which naturally arises from the free rigid body dynamics.

Citations

• Die Fundamentalgruppe des Raumes der regul�ren Orbits einer endlichen komplexen Spiegelungsgruppe

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