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

Junmin Yang; Maoan Han

doi:10.3934/dcds.2009.24.827

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2009, Volume 24, Issue 3: 827-840. Doi: 10.3934/dcds.2009.24.827

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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

Received: September 30, 2007

Revised: October 31, 2008

Published: August 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 34C05, 34C07; Secondary: 37G45.

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