Rigid Polynomial Differential Systems with Homogeneous Nonlinearities

Autor:	Jaume Llibre
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	quadratic systems quadratic differential systems limit cycles rigid system rigid differential systems Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 18, p 2806 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12182806
Popis:	Planar differential systems whose angular velocity is constant are called rigid or uniform differential systems. The first rigid system goes back to the pendulum clock of Christiaan Huygens in 1656; since then, the interest for the rigid systems has been growing. Thus, at this moment, in MathSciNet there are 108 articles with the words rigid systems or uniform systems in their titles. Here, we study the dynamics of the planar rigid polynomial differential systems with homogeneous nonlinearities of arbitrary degree. More precisely, we characterize the existence and non-existence of limit cycles in this class of rigid systems, and we determine the local phase portraits of their finite and infinite equilibrium points in the Poincaré disc. Finally, we classify the global phase portraits in the Poincaré disc of the rigid polynomial differential systems of degree two, and of one class of rigid polynomial differential systems with cubic homogeneous nonlinearities that can exhibit one limit cycle.
Databáze:	Directory of Open Access Journals
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