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August  2009, 24(3): 827-840. doi: 10.3934/dcds.2009.24.827

On the number of limit cycles of a cubic Near-Hamiltonian system

Junmin Yang 1, and  Maoan Han 1,

1. 

Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

Received  October 2007 Revised  November 2008 Published  April 2009

For the near-Hamiltonian system $\dot{x}=y+\varepsilon P(x,y),\dot{y}=x-x^2+\varepsilon Q(x,y)$, where $P$ and $Q$ are polynomials of $x,y$ having degree 3 with varying coefficients we obtain 5 limit cycles.
Keywords: homoclinic loop., limit cycle, polynomial.
Mathematics Subject Classification: Primary: 34C05, 34C07; Secondary: 37G4.
Citation: Junmin Yang, Maoan Han. On the number of limit cycles of a cubic Near-Hamiltonian system. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 827-840. doi: 10.3934/dcds.2009.24.827
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