کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4609235 1413558 2017 53 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Beyond the Melnikov method: A computer assisted approach
ترجمه فارسی عنوان
فراتر از روش Melnikov: d؛ یک رویکرد با کمک کامپیوتر
کلمات کلیدی
روش Melnikov؛ منیفولدهای ثابت به طور معمول هذلولی. تقاطع متقاطع هموکلینیک؛ اثبات به کمک کامپیوتر
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی

We present a Melnikov type approach for establishing transversal intersections of stable/unstable manifolds of perturbed normally hyperbolic invariant manifolds (NHIMs). The method is based on a new geometric proof of the normally hyperbolic invariant manifold theorem, which establishes the existence of a NHIM, together with its associated invariant manifolds and bounds on their first and second derivatives. We do not need to know the explicit formulas for the homoclinic orbits prior to the perturbation. We also do not need to compute any integrals along such homoclinics. All needed bounds are established using rigorous computer assisted numerics. Lastly, and most importantly, the method establishes intersections for an explicit range of parameters, and not only for perturbations that are ‘small enough’, as is the case in the classical Melnikov approach.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 262, Issue 1, 5 January 2017, Pages 365–417
نویسندگان
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