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The Polar oscillator is the dynamical system defined by the equations (in polar coordinates):

$$ \begin{cases} \dot\rho=\lambda(\rho_\infty-\rho)\\ \dot\theta = \frac{2\pi}{T} \end{cases} $$

In cartesian coordinates this becomes, for $$T=1$$ and $$\rho_\infty=1$$:

$$ \begin{cases} \dot x= \frac{x}{\sqrt{x^2+y^2}} - 2\pi y - \frac{1}{\lambda}     \\ \dot y= \frac{y}{\sqrt{x^2+y^2}} + 2\pi x - \frac{1}{\lambda} \end{cases} $$