Experimental results for the Poincaré center problem (including an Appendix with Martin Cremer)
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 Zoladek's conjecture about general degree 3 non linearities
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2005
 DOI:
 10.48550/arXiv.math/0505547
 arXiv:
 arXiv:math/0505547
 Bibcode:
 2005math......5547B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Dynamical Systems;
 34C05;
 12E05
 EPrint:
 16 pages, 2 figures, source code of programs at http://wwwifm.math.unihannover.de/~bothmer/strudel/. Added references, the result of Example 6.2 is not new. Added two new sections on rationally reversible systems. The 4th codim 7 component we saw only experimentally can now also be identified geometricaly