期刊
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
卷 13, 期 1, 页码 47-106出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127403006352
关键词
real algebraic curve; scheme of ovals; limit cycle; bifurcation of vector fields; configuration of limit cycles; Hilbert number H(n)
The original Hilbert's 16th problem can be split into four parts consisting of Problems A-D. In this paper, the progress of study on Hilbert's 16th problem is presented, and the relationship between Hilbert's 16th problem and bifurcations of planar vector fields is discussed. The material is presented in eight sections. Section 1: Introduction: what is Hilbert's 16th problem? Section 2: The first part of Hilbert's 16th problem. Section 3: The second part of Hilbert's 16th problem: introduction. Section 4: Focal values, saddle values and finite cyclicity in a fine focus, closed orbit and homoclinic loop. Section 5: Finiteness problem. Section 6: The weakened Hilbert's 16th problem. Section 7: Global and local bifurcations of Z(q)-equivariant vector fields. Section 8: The rate of growth of Hilbert number H(n) with n.
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