Communications in Mathematical Physics

, Volume 48, Issue 1, pp 53–79 | Cite as

On resonant non linearly coupled oscillators with two equal frequencies

  • Martin Kummer


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 inR4,\(\mathcal{O}_3 \) representing a convergent power series that begins with a third order term.

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


Neural Network Statistical Physic Complex System Periodic Orbit Nonlinear Dynamics 
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 1976

Authors and Affiliations

  • Martin Kummer
    • 1
  1. 1.Department of MathematicsThe University of ToledoToledoUSA

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