Experimental results for the Poincar\'e center problem (including an Appendix with Martin Cremer)
Algebraic Geometry
2009-07-10 v2 Dynamical Systems
Abstract
We apply a heuristic method based on counting points over finite fields to the Poincar\'e 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
Cite
@article{arxiv.math/0505547,
title = {Experimental results for the Poincar\'e center problem (including an Appendix with Martin Cremer)},
author = {Hans-Christian Graf v. Bothmer},
journal= {arXiv preprint arXiv:math/0505547},
year = {2009}
}
Comments
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