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Experimental results for the Poincaré center problem

  • Hans-Christian Graf Von Bothmer
Article

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.

2000 Mathematics Subject Classification:

34C05 12E05 

Keywords:

Poincaré center computer algebra finite fields 

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Copyright information

© Birkhaueser 2007

Authors and Affiliations

  • Hans-Christian Graf Von Bothmer
    • 1
  1. 1.Institut für Algebraische GeometrieUniversitat HannoverHannoverGermany

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