کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9501846 | 1338793 | 2005 | 36 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the number of zeros of Abelian integrals for a polynomial Hamiltonian irregular at infinity
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: On the number of zeros of Abelian integrals for a polynomial Hamiltonian irregular at infinity On the number of zeros of Abelian integrals for a polynomial Hamiltonian irregular at infinity](/preview/png/9501846.png)
چکیده انگلیسی
Up to now, most of the results on the tangential Hilbert 16th problem have been concerned with the Hamiltonian regular at infinity, i.e., its principal homogeneous part is a product of the pairwise different linear forms. In this paper, we study a polynomial Hamiltonian which is not regular at infinity. It is shown that the space of Abelian integral for this Hamiltonian is finitely generated as a R[h] module by several basic integrals which satisfy the Picard-Fuchs system of linear differential equations. Applying the bound meandering principle, an upper bound for the number of complex isolated zeros of Abelian integrals is obtained on a positive distance from critical locus. This result is a partial solution of tangential Hilbert 16th problem for this Hamiltonian. As a consequence, we get an upper bound of the number of limit cycles produced by the period annulus of the non-Hamiltonian integrable quadratic systems whose almost all orbits are algebraic curves of degree k+n, under polynomial perturbation of arbitrary degree.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 209, Issue 2, 15 February 2005, Pages 329-364
Journal: Journal of Differential Equations - Volume 209, Issue 2, 15 February 2005, Pages 329-364
نویسندگان
Yulin Zhao,