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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.

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closed as too localized by Andrés E. Caicedo, Rahul, J. M., Akhil Mathew Apr 6 '11 at 15:28

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

You might want to edit the title of this question. – Jesse Madnick Apr 5 '11 at 7:33
Why did you delete the body of the question? – Rahul Apr 6 '11 at 6:15
in general it is vastly preferable that we keep the contents of question statements as self-contained on this website as possible. Therefore I reverted your edit which replaced the above question Text with a Linked Image. Your edits to this question may be interpreted as borderline vandalism, please refrain from that in the future. – Willie Wong Apr 6 '11 at 12:54
Please do not ask questions in imperative. – user5501 Apr 6 '11 at 13:08

$re^{i\theta} \longrightarrow re^{i(\theta+ (-1)^{[\frac{r}{2 \pi}]}r)} $

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start with circles $(r\cos\theta,r\sin\theta)\mapsto(-\sin\theta,\cos\theta)$. now vary the magnitude, say by $\sin r$: $$ (r\cos\theta,r\sin\theta)\mapsto(\sin r)(-\sin\theta,\cos\theta) $$

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