POLYNOMIAL SYSTEMS - A LOWER-BOUND FOR THE HILBERT-NUMBERS

被引：68

作者：

CHRISTOPHER, CJ

LLOYD, NG

机构：

[1] Dept of Maths, Univ of Wales, Aberystwyth

来源：

PROCEEDINGS OF THE ROYAL SOCIETY-MATHEMATICAL AND PHYSICAL SCIENCES | 1995年 / 450卷 / 1938期

关键词：

D O I：

10.1098/rspa.1995.0081

中图分类号：

学科分类号：

摘要：

Let H-n be the maximum possible number of limit cycles of systems x= P(x, y), y = Q(x, y), where P and Q are polynomials of degree at most n. We are concerned with the rate of growth of H-n as n increases: it is known that H-n greater than or equal to kn(2) for some constant k. In this paper we show that H-n grows at least as rapidly as n(2) log n.

引用

页码：219 / 224

页数：6

共 13 条

[1] Basarab-Horwath P, 1988, NIEUW ARCH WISK, V6, P295
[2] ECALLE J, 1987, CR ACAD SCI I-MATH, V304, P375
[3] ECALLE J, 1987, CR ACAD SCI I-MATH, V304, P431
[4] Guckenheimer J., 2013, APPL MATH SCI, DOI 10.1007/978-1-4612- 1140-2
[5] ILYASHENKO YS, 1969, MATH USSR SB, V7, P353
[6] LANDIS EM, 1960, AM MATH SOC TRANSL, V14, P181
[7] LANDIS EM, 1958, AM MATH SOC TRANSL, V10, P177
[8] LI J, 1985, ACTA MATH SINICA, V28, P509
[9] LLOYD NG, 1988, LONDON MATH SOC LECT, V127, P192
[10] Otrokov N.F., 1954, MAT SBORNIK, V34, P127

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