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Title: Analytic extension of Birkhoff normal forms for Hamiltonian systems of one degree of freedom : Simple pendulum and free rigid body dynamics (Exponential Analysis of Differential Equations and Related Topics)
Authors: Tarama, Daisuke
Francoise, Jean-Pierre
Keywords: 14D06
Birkhoff normal form
analytic extension
free rigid body
simple pendulum
elliptic fibration
Issue Date: Nov-2014
Publisher: Research Institute for Mathematical Sciences, Kyoto University
Journal title: 数理解析研究所講究録別冊
Volume: B52
Start page: 219
End page: 236
Abstract: Birkhoff normal form is a power series expansion associated with the local behavior of a Hamiltonian system near the critical point. It is known that one can take convergent canonical transformation which puts the Hamiltonian into Birkhoff normal form 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 two examples of Hamiltonian systems of one degree of freedom, the simple pendulum dynamics and the free rigid body dynamics on SO(3). It is shown that the analytic continuation of the inverse derivative for the Birkhoff normal forms has monodromy structure, which is explicitly calculated, and that in the free rigid body case the monodromy coincides with that of an elliptic fibration which naturally arises from the dynamics.
Description: "Exponential Analysis of Differential Equations and Related Topics". October 15~18, 2013. edited by Yoshitsugu Takei. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.
Rights: © 2014 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.
Appears in Collections:B52 Exponential Analysis of Differential Equations and Related Topics

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