Centers of quasi-homogeneous polynomial differential equations of degree three

We characterize the centers of the quasi-homogeneous planar polynomial differential systems of degree three. Such systems do not admit isochronous centers. At most one limit cycle can bifurcate from the periodic orbits of a center of a cubic homogeneous polynomial system using the averaging theory o...

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Bibliographic Details
Authors: Aziz, Waleed|||0000-0003-4529-7947, Llibre, Jaume|||0000-0002-9511-5999, Pantazi, Chara|||0000-0002-4394-404X
Format: article
Publication Date:2014
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:150718
Online Access:https://ddd.uab.cat/record/150718
https://dx.doi.org/urn:doi:10.1016/j.aim.2013.12.006
Access Level:Open access
Keyword:Quasi-homogeneous polynomial systems
Centers
Limit cycles
Description
Summary:We characterize the centers of the quasi-homogeneous planar polynomial differential systems of degree three. Such systems do not admit isochronous centers. At most one limit cycle can bifurcate from the periodic orbits of a center of a cubic homogeneous polynomial system using the averaging theory of first order.