| NEW FAMILIES OF CENTERS AND LIMIT CYCLES FOR POLYNOMIAL DIFFERENTIAL SYSTEMS WITH HOMOGENEOUS NONLINEARITIES |
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| 作者姓名： | 李承治 李伟固 Jaume Llibre 张芷芬 |
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| 作者单位： | School of Maih. Sciences，Peking University，Beijing 100871，School of Maih. Sciences，Peking University，Beijing 100871，Dept. de Matematiques，Universitat Autonoma de Barcelona，Bellaterra，08193 Barcelona，Spain，School of Maih. Sciences，Peking University，Beijing 100871 |
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| 基金项目： | The first and last authors are partially supported by NSFC and RFDP of China, the second author is partially supported by the 973 Project of the Ministry of Science and Technologe of China, the third author is partially supported by a DGES grant number B |
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| 摘 要： | We consider the class of polynomial differential equations x = -y+Pn(x,y), y = x + Qn(x, y), where Pn and Qn are homogeneous polynomials of degree n. Inside this class we identify a new subclass of systems having a center at the origin. We show that this subclass contains at least two subfamilies of isochro-nous centers. By using a method different from the classical ones, we study the limit cycles that bifurcate from the periodic orbits of such centers when we perturb them inside the class of all polynomial differential systems of the above form. In particular, we present a function whose simple zeros correspond to the limit cycles vvhich bifurcate from the periodic orbits of Hamiltonian systems.
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NEW FAMILIES OF CENTERS AND LIMIT CYCLES FOR POLYNOMIAL DIFFERENTIAL SYSTEMS WITH HOMOGENEOUS NONLINEARITIES |
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| Li Chengzhi.NEW FAMILIES OF CENTERS AND LIMIT CYCLES FOR POLYNOMIAL DIFFERENTIAL SYSTEMS WITH HOMOGENEOUS NONLINEARITIES[J].微分方程年刊(英文版),2003(3). |
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| Authors: | Li Chengzhi |
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| Abstract: | We consider the class of polynomial differential equations x = -y+Pn(x,y), y = x + Qn(x, y), where Pn and Qn are homogeneous polynomials of degree n. Inside this class we identify a new subclass of systems having a center at the origin. We show that this subclass contains at least two subfamilies of isochro-nous centers. By using a method different from the classical ones, we study the limit cycles that bifurcate from the periodic orbits of such centers when we perturb them inside the class of all polynomial differential systems of the above form. In particular, we present a function whose simple zeros correspond to the limit cycles vvhich bifurcate from the periodic orbits of Hamiltonian systems. |
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| Keywords: | limit cycles centers bifurcation |
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