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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
A criticality result for polycycles in a family of quadratic reversible centers
چکیده انگلیسی
We consider the family of dehomogenized Loud's centers Xμ=y(x−1)∂x+(x+Dx2+Fy2)∂y, where μ=(D,F)∈R2, 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,μ∈R2} 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 ΓB of codimension 1 in R2. In the present paper we succeed in proving that a subset of ΓB 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
نویسندگان
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