Nonintegrability in the Vicinity of an Equilibrium Position

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


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.


Power Series Hamiltonian System Equilibrium Position Hamiltonian Function Homogeneous Form 
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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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