摘要
We study a class of quartic polynomial Poincare equations by applying a recurrence formula of focal value. We give the necessary and sufficient conditions for the origin to be a center, and prove that the order of fine focus at the origin for this class of equations is at most 6. Key words quartic polynomial Poincare equation - center - fine focus - order CLC number O 175. 12 Foundation item: Supported by the National Natural Science Foundation of China (19531070)Biography: TIAN De-sheng (1966-), male, Ph. D candidate, research direction: qualitative theory of differential equation.
We study a class of quartic polynomial Poincare equations by applying a recurrence formula of focal value. We give the necessary and sufficient conditions for the origin to be a center, and prove that the order of fine focus at the origin for this class of equations is at most 6. Key words quartic polynomial Poincare equation - center - fine focus - order CLC number O 175. 12 Foundation item: Supported by the National Natural Science Foundation of China (19531070)Biography: TIAN De-sheng (1966-), male, Ph. D candidate, research direction: qualitative theory of differential equation.
基金
theNationalNaturalScienceFoundationofChina (1 9531 0 70 )
