| Invariant algebraic curves and rational first integrals of holomorphic foliations in CP(2) |
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| 引用本文： | 张祥. Invariant algebraic curves and rational first integrals of holomorphic foliations in CP(2)[J]. 中国科学A辑(英文版), 2003, 46(2). DOI: 10.1360/03ys9029 |
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| 作者姓名： | 张祥 |
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| 作者单位： | Department of |
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| 基金项目： | This work was partially supported by the National Natural Science Foundation of China (Grant No. 19901013). |
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| 摘 要： | In this paper, using the tools of algebraic geometry we provide sufficient conditions for a holomor-phic foliation in CP(2) to have a rational first integral. Moreover, we obtain an upper bound of the degrees of invariant algebraic curves of a holomorphic foliation in CP(2). Then we use these results to prove that any holomorphic foliation of degree 2 does not have cubic limit cycles.
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Invariant algebraic curves and rational first integrals of holomorphic foliations in CP(2) |
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| ZHANG Xiang. Invariant algebraic curves and rational first integrals of holomorphic foliations in CP(2)[J]. Science in China(Mathematics), 2003, 46(2). DOI: 10.1360/03ys9029 |
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| Authors: | ZHANG Xiang |
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| Affiliation: | Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, China |
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| Abstract: | In this paper, using the tools of algebraic geometry we provide sufficient conditions for a holomor-phic foliation in CP(2) to have a rational first integral. Moreover, we obtain an upper bound of the degrees of invariant algebraic curves of a holomorphic foliation in CP(2). Then we use these results to prove that any holomorphic foliation of degree 2 does not have cubic limit cycles. |
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| Keywords: | holomorphic foliation invariant algebraic curve rational first integral cubic limit cycle. |
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