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Spring 2012 Existence of divergent Birkhoff normal forms of Hamiltonian functions
Xianghong Gong
Illinois J. Math. 56(1): 85-94 (Spring 2012). DOI: 10.1215/ijm/1380287461

Abstract

By the work of Siegel it is well known that as a rule the Birkhoff normal form of a real analytic Hamiltonian system whose eigenvalues satisfies suitable non-resonance condition cannot be realized by convergent symplectic transformations. We show the existence of divergent Birkhoff normal forms for suitable Hamiltonian systems. Our calculation shows how the small divisors appear in the normal forms, from which the divergence is derived by using Siegel’s methods of small divisors.

Citation

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Xianghong Gong. "Existence of divergent Birkhoff normal forms of Hamiltonian functions." Illinois J. Math. 56 (1) 85 - 94, Spring 2012. https://doi.org/10.1215/ijm/1380287461

Information

Published: Spring 2012
First available in Project Euclid: 27 September 2013

zbMATH: 1309.37053
MathSciNet: MR3117019
Digital Object Identifier: 10.1215/ijm/1380287461

Subjects:
Primary: 37J40

Rights: Copyright © 2012 University of Illinois at Urbana-Champaign

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Vol.56 • No. 1 • Spring 2012
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