Using polar coordinates, create a system with a fixed point at the origin, and with infinitely many periodic orbits which alternate between clockwise and counterclockwise flows.
Polar coordinates questions
2
$\begingroup$
dynamical-systems
-
1Please do not ask questions in imperative. – 2011-04-06
2 Answers
1
$re^{i\theta} \longrightarrow re^{i(\theta+ (-1)^{[\frac{r}{2 \pi}]}r)} $
0
start with circles $(r\cos\theta,r\sin\theta)\mapsto(-\sin\theta,\cos\theta)$. now vary the magnitude, say by $\sin r$: $ (r\cos\theta,r\sin\theta)\mapsto(\sin r)(-\sin\theta,\cos\theta) $