کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898776 | 1631499 | 2018 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A criticality result for polycycles in a family of quadratic reversible centers
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: A criticality result for polycycles in a family of quadratic reversible centers A criticality result for polycycles in a family of quadratic reversible centers](/preview/png/8898776.png)
چکیده انگلیسی
We consider the family of dehomogenized Loud's centers Xμ=y(xâ1)âx+(x+Dx2+Fy2)ây, where μ=(D,F)âR2, and we study the number of critical periodic orbits that emerge or disappear from the polycycle at the boundary of the period annulus. This number is defined exactly the same way as the well-known notion of cyclicity of a limit periodic set and we call it criticality. The previous results on the issue for the family {Xμ,μâR2} distinguish between parameters with criticality equal to zero (regular parameters) and those with criticality greater than zero (bifurcation parameters). A challenging problem not tackled so far is the computation of the criticality of the bifurcation parameters, which form a set ÎB of codimension 1 in R2. In the present paper we succeed in proving that a subset of ÎB has criticality equal to one.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 264, Issue 11, 5 June 2018, Pages 6585-6602
Journal: Journal of Differential Equations - Volume 264, Issue 11, 5 June 2018, Pages 6585-6602
نویسندگان
D. Rojas, J. Villadelprat,