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.
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© 1996 Springer-Verlag Berlin Heidelberg
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Kozlov, V.V. (1996). Nonintegrability in the Vicinity of an Equilibrium Position. In: Symmetries, Topology and Resonances in Hamiltonian Mechanics. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78393-7_7
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DOI: https://doi.org/10.1007/978-3-642-78393-7_7
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