- #1
squenshl
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Homework Statement
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)
Homework Equations
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.