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Nonintegrability in the Vicinity of an Equilibrium Position

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Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 31)

Abstract

There is another method of proving nonintegrability. It is based on estimates from below for coefficients of the power series representing formal integrals which exist by Birkhoff’s theorem. It turns out that the reason for divergence of such series is the existence of anomalously small denominators, i.e., almost resonance relations between the frequencies of small oscillations near equilibria.

Keywords

Power Series Hamiltonian System Equilibrium Position Hamiltonian Function Homogeneous Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  1. 1.Department of MathematicsMoscow State UniversityMoscowRussia

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