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Nonintegrability of Hamiltonian Systems Close to Integrable Ones

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

Abstract

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
$$ H=H_0 (y_1 , \ldots ,y_n )+\varepsilon H_1(x_1,\ldots ,x_n ,y_1\ldots ,y_n )+\cdots.$$

Keywords

Periodic Solution Hamiltonian System Formal Power Series Trigonometric Polynomial Hamiltonian Function 
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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