Nonintegrability of Hamiltonian Systems Close to Integrable Ones
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 31)
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We begin the consideration of the analytic obstacles to integrability with the analysis of Poincaré’s “basic problem of dynamics”. This problem deals with the Hamiltonian system whose Hamiltonian has the form
$$ H=H_0 (y_1 , \ldots ,y_n )+\varepsilon H_1(x_1,\ldots ,x_n ,y_1\ldots ,y_n )+\cdots.$$
KeywordsPeriodic Solution Hamiltonian System Formal Power Series Trigonometric Polynomial Hamiltonian Function
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© Springer-Verlag Berlin Heidelberg 1996