1. The problem statement, all variables and given/known data Prove that the following system has at least one periodic orbit. x' = x - y - 2x3 - 2xy2 + x2sqrt(x2 + y2) y' = x + y - 2x2y - 2y3 + xysqrt(x2 + y2) 2. Relevant equations 3. The attempt at a solution I converted to polar coordinates to get r' = (xx'+yy')/r and theta' = (xy'-yx')/r2 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.