کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5778884 | 1413742 | 2016 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Geometry of slow-fast Hamiltonian systems and Painlevé equations
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In the first part of the paper we introduce some geometric tools needed to describe slow-fast Hamiltonian systems on smooth manifolds. We start with a smooth bundle p:MâB where (M,Ï) is a Câ-smooth presymplectic manifold with a closed constant rank 2-form Ï and (B,λ) is a smooth symplectic manifold. The 2-form Ï is supposed to be compatible with the structure of the bundle, that is the bundle fibers are symplectic manifolds with respect to the 2-form Ï and the distribution on M generated by kernels of Ï is transverse to the tangent spaces of the leaves and the dimensions of the kernels and of the leaves are supplementary. This allows one to define a symplectic structure Ωε=Ï+εâ1pâλ on M for any positive small ε, where pâλ is the lift of the 2-form λ to M. Given a smooth Hamiltonian H on M one gets a slow-fast Hamiltonian system with respect to Ωε. We define a slow manifold SM for this system. Assuming SM is a smooth submanifold, we define a slow Hamiltonian flow on SM. The second part of the paper deals with singularities of the restriction of p to SM. We show that if dimM=4,dimB=2 and Hamilton function H is generic, then the behavior of the system near a singularity of fold type is described, to the main order, by the equation Painlevé-I, and if this singularity is a cusp, then the related equation is Painlevé-II.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Indagationes Mathematicae - Volume 27, Issue 5, December 2016, Pages 1219-1244
Journal: Indagationes Mathematicae - Volume 27, Issue 5, December 2016, Pages 1219-1244
نویسندگان
L.M. Lerman, E.I. Yakovlev,