On the configurations of centers of planar Hamiltonian Kolmogorov cubic polynomial differential systems

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 $x y (a + b x + c y + d x^{2} + e x y + f y^{2}) = h$ has at most four families of level ovals in $ℝ^{2}$ for all real parameters $a, b, c, d, e, f$ and $h$ .

PDF Access Denied

We have not been able to recognize your IP address 3.15.147.215 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

Hamiltonian system, Kolmogorov systems, cubic polynomial differential systems, centers, configuration of centers

Mathematical Subject Classification 2010

Primary: 37K10, 37C27

Secondary: 37K05

Milestones

Received: 13 December 2017

Revised: 2 April 2019

Accepted: 4 February 2020

Published: 13 July 2020

Authors

Jaume Llibre
Departament de Matemàtiques Universitat Autònoma de Barcelona Barcelona Spain

Dongmei Xiao
School of Mathematical Sciences Shanghai Jiao Tong University Shanghai China

Vol. 306, No. 2, 2020

Jaume Llibre and Dongmei Xiao

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors