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Oct 23, 2011 at 5:54 comment added Robert Bryant @Vladimir: First, you shouldn't be using 'answer' to make comments unless you explicitly identify your 'answer' as a long comment; this causes the answer counts to be bad. Second, to respond to your question, the answer is 'yes', there exist many smooth integral curves different from the ellipse satisfying the desired conditions. Also, it's almost certainly true that there are analytic examples other than the ellipse. I haven't verified this, but I can't imagine what could go wrong with a proof.
Oct 21, 2011 at 1:47 history answered Vladimir Georgiev CC BY-SA 3.0