Experimental results for the Poincaré center problem
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We apply a heuristic method based on counting points over finite fields to the Poincaré center problem. We show that this method gives the correct results for homogeneous non linearities of degree 2 and 3. Also we obtain new evidence for Żoła̧dek’s conjecture about general degree 3 non linearities.
2000 Mathematics Subject Classification:34C05 12E05
Keywords:Poincaré center computer algebra finite fields
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