کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4611599 | 1338631 | 2012 | 27 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Lower bounds for the Hilbert number of polynomial systems
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let H(m) denote the maximal number of limit cycles of polynomial systems of degree m. It is called the Hilbert number. The main part of Hilbertʼs 16th problem posed in 1900 is to find its value. The problem is still open even for m=2. However, there have been many interesting results on the lower bound of it for m⩾2. In this paper, we give some new lower bounds of this number. The results obtained in this paper improve all existing results for all m⩾7 based on some known results for m=3,4,5,6. In particular, we obtain that H(m) grows at least as rapidly as for all large m.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 252, Issue 4, 15 February 2012, Pages 3278-3304
Journal: Journal of Differential Equations - Volume 252, Issue 4, 15 February 2012, Pages 3278-3304