# 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 induces in

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

*R*^{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.

## Keywords

Neural Network Statistical Physic Complex System Periodic Orbit Nonlinear Dynamics
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