کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9518015 | 1345510 | 2005 | 90 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A Morse complex for infinite dimensional manifolds-part I
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
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چکیده انگلیسی
In this paper and in the forthcoming Part II, we introduce a Morse complex for a class of functions f defined on an infinite dimensional Hilbert manifold M, possibly having critical points of infinite Morse index and co-index. The idea is to consider an infinite dimensional subbundle-or more generally an essential subbundle-of the tangent bundle of M, suitably related with the gradient flow of f. This Part I deals with the following questions about the intersection W of the unstable manifold of a critical point x and the stable manifold of another critical point y: finite dimensionality of W, possibility that different components of W have different dimension, orientability of W and coherence in the choice of an orientation, compactness of the closure of W, classification, up to topological conjugacy, of the gradient flow on the closure of W, in the case dimW=2.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 197, Issue 2, 10 November 2005, Pages 321-410
Journal: Advances in Mathematics - Volume 197, Issue 2, 10 November 2005, Pages 321-410
نویسندگان
Alberto Abbondandolo, Pietro Majer,