#### Vol. 306, No. 2, 2020

 Recent Issues Vol. 307: 1  2 Vol. 306: 1  2 Vol. 305: 1  2 Vol. 304: 1  2 Vol. 303: 1  2 Vol. 302: 1  2 Vol. 301: 1  2 Vol. 300: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Contacts Submission Guidelines Submission Form Policies for Authors ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Special Issues Author Index To Appear Other MSP Journals
On the configurations of centers of planar Hamiltonian Kolmogorov cubic polynomial differential systems

### Jaume Llibre and Dongmei Xiao

Vol. 306 (2020), No. 2, 611–644
##### Abstract

We study the kind of centers that Hamiltonian Kolmogorov cubic polynomial differential systems can exhibit. Moreover, we analyze the possible configurations of these centers with respect to the invariant coordinate axes, and obtain that the real algebraic curve $xy\left(a+bx+cy+d{x}^{2}+exy+f{y}^{2}\right)=h$ has at most four families of level ovals in ${ℝ}^{2}$ for all real parameters $a,b,c,d,e,f$ and $h$.

##### Keywords
Hamiltonian system, Kolmogorov systems, cubic polynomial differential systems, centers, configuration of centers
##### Mathematical Subject Classification 2010
Primary: 37K10, 37C27
Secondary: 37K05