(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that the following system has at least one periodic orbit.

x' = x - y - 2x^{3}- 2xy^{2}+ x^{2}sqrt(x^{2}+ y^{2})

y' = x + y - 2x^{2}y - 2y^{3}+ xysqrt(x^{2}+ y^{2})

2. Relevant equations

3. The attempt at a solution

I converted to polar coordinates to get r' = (xx'+yy')/r and theta' = (xy'-yx')/r^{2}

For r' I got something ugly but in terms of theta' I get theta' = 1. If theta' = 1 = constant imply a periodic orbit? Any help please.

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# Homework Help: Periodic orbit

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