کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6417176 1338533 2015 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Perturbation theory of a symmetric center within Liénard equations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Perturbation theory of a symmetric center within Liénard equations
چکیده انگلیسی

In this article, we introduce the use of Lambert function to develop further the global perturbation theory of an integrable Liénard equation which displays a symmetric center. We prove a global Morse lemma for the first integral and deduce the existence of an associated Picard-Fuchs system. We revisit previous contributions to first-order perturbation theory with the help of these new analytic techniques and in particular, we check that the fundamental integrals are linearly independent. The Lambert function allows to find an expansion formula for these integrals. We also study the possibility to develop a higher-order perturbation theory. The algorithm of the successive derivatives works in general in the class of analytic functions on the domain D where the level sets of the first integral are ovals. We end the article with some results on the first integral of a symmetric Liénard equation deduced from the algorithm of successive derivatives.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 259, Issue 6, 15 September 2015, Pages 2408-2429
نویسندگان
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