Geometry of planar quadratic systems
摘要
In this paper, the global qualitative analysis of planar quadratic dynamical systems is established and a new geometric approach to solving Hilbert's Sixteenth Problem in this special case of polynomial systems is suggested. Using geometric properties of four field rotation parameters of a new canonical system which is constructed in this paper, we present a proof of our earlier conjecture that the maximum number of limit cycles in a quadratic system is equal to four and the only possible their distribution is (3:1). Besides, applying the Wintner-Perko termination principle for multiple limit cycles to our canonical system, we prove in a different way that a quadratic system has at most three limit cycles around a singular point (focus) and give another proof of the same conjecture.
引用
@article{arxiv.math/0611142,
title = {Geometry of planar quadratic systems},
author = {Valery A. Gaiko},
journal= {arXiv preprint arXiv:math/0611142},
year = {2007}
}
备注
13 pages