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Experimental results for the Poincaré center problem

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Nonlinear Differential Equations and Applications NoDEA Aims and scope Submit manuscript

Abstract.

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.

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  1. Institut für Algebraische Geometrie, Universitat Hannover, Welfengarten 1, D-30167, Hannover, Germany

    Hans-Christian Graf Von Bothmer

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  1. Hans-Christian Graf Von Bothmer
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Von Bothmer, HC.G. Experimental results for the Poincaré center problem. Nonlinear differ. equ. appl. 14, 671–698 (2007). https://doi.org/10.1007/s00030-007-5036-x

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  • DOI: https://doi.org/10.1007/s00030-007-5036-x

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