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On resonant non linearly coupled oscillators with two equal frequencies

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Abstract

This paper contains a detailed study of the flow that the classical Hamiltonian

$$H = \tfrac{1}{2}(x\begin{array}{*{20}c} 2 \\ 1 \\ \end{array} + y\begin{array}{*{20}c} 2 \\ 1 \\ \end{array} ) + \tfrac{1}{2}(x\begin{array}{*{20}c} 2 \\ 2 \\ \end{array} + y\begin{array}{*{20}c} 2 \\ 2 \\ \end{array} ) + \mathcal{O}_3 $$

induces inR 4,\(\mathcal{O}_3 \) representing a convergent power series that begins with a third order term.

In particular the existence and stability of periodic orbits is investigated.

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Authors and Affiliations

  1. Department of Mathematics, The University of Toledo, 43606, Toledo, Ohio, USA

    Martin Kummer

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  1. Martin Kummer
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Communicated by J. Moser

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Kummer, M. On resonant non linearly coupled oscillators with two equal frequencies. Commun.Math. Phys. 48, 53–79 (1976). https://doi.org/10.1007/BF01609411

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