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

DOI10.2140/pjm.2020.306.611zbMath1453.37054OpenAlexW3043767843MaRDI QIDQ785743

Dongmei Xiao, Jaume Llibre

Publication date: 10 August 2020

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/232598

zbMATH Keywords

Hamiltonian systemcentersKolmogorov systemscubic polynomial differential systemsconfiguration of centers

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Periodic orbits of vector fields and flows (37C27) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25)

Related Items (1)

Configuration of planar Kolmogorov cubic polynomial differential systems with the most centers

Cites Work

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• Phase portraits of reversible linear differential systems with cubic homogeneous polynomial nonlinearities having a non-degenerate center at the origin
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• Dynamics, integrability and topology for some classes of Kolmogorov Hamiltonian systems in \(\mathbb{R}_+^4\)
• On the differential equations of species in competition
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• Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields
• Algebraic Particular Integrals, Integrability and the Problem of the Center
• Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point
• Centennial History of Hilbert's 16th Problem
• Centers: their integrability and relations with the divergence
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• On a certain generalization of Bautin's theorem
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