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:
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arXiv Mathematics e-prints
- Pub Date:
- May 2005
- DOI:
- arXiv:
- arXiv:math/0505547
- Bibcode:
- 2005math......5547B
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Dynamical Systems;
- 34C05;
- 12E05
- E-Print:
- 16 pages, 2 figures, source code of programs at http://www-ifm.math.uni-hannover.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