کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8899135 | 1631511 | 2017 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In this paper we introduce a new compactness condition - Property-(C) - for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying the this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain the E-cohomological Conley index. We formulate a continuation principle for the E-cohomological Conley index and show that all LS-flows can be continued to LS-gradient flows. We show that the Morse homology of LS-gradient flows computes the E-cohomological Conley index. We use Lyapunov functions to define the Morse-Conley-Floer cohomology in this context, and show that it is also isomorphic to the E-cohomological Conley index.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 263, Issue 11, 5 December 2017, Pages 7162-7186
Journal: Journal of Differential Equations - Volume 263, Issue 11, 5 December 2017, Pages 7162-7186
نویسندگان
Marek Izydorek, Thomas O. Rot, Maciej Starostka, Marcin Styborski, Robert C.A.M. Vandervorst,