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Search: MSC category 34D30 ( Structural stability and analogous concepts [See also 37C20] )

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1. CMB 2015 (vol 58 pp. 818)

Llibre, Jaume; Zhang, Xiang
 On the Limit Cycles of Linear Differential Systems with Homogeneous Nonlinearities We consider the class of polynomial differential systems of the form $\dot x= \lambda x-y+P_n(x,y)$, $\dot y=x+\lambda y+ Q_n(x,y),$ where $P_n$ and $Q_n$ are homogeneous polynomials of degree $n$. For this class of differential systems we summarize the known results for the existence of limit cycles, and we provide new results for their nonexistence and existence. Keywords:polynomial differential system, limit cycles, differential equations on the cylinderCategories:34C35, 34D30

2. CMB 2002 (vol 45 pp. 355)

Cresson, Jacky
 Obstruction Ã  la linÃ©arisation des champs de vecteurs polynomiaux On explicite une classe de champ de vecteurs polynomiaux non analytiquement lin\'earisables \a l'aide de la correction introduite par \'Ecalle-Vallet. Notamment, on \'etend des r\'esultats de Schuman sur la trivialit\'e des hamiltoniens homog\enes isochrones. We characterize a class of polynomial vector fields which are not analytically linearizable using the correction introduced by \'Ecalle-Vallet. Then, we extend Schuman's result about non existence of isochronous homogenous Hamiltonian systems. Keywords:linÃ©arisation-problÃ¨me du centre-hamiltonien-darboux-champs polynomiauxCategories:34D10, 34D30
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