کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
840629 908486 2012 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An estimate on the fractal dimension of attractors of gradient-like dynamical systems
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
An estimate on the fractal dimension of attractors of gradient-like dynamical systems
چکیده انگلیسی

This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like semigroups in a general Banach space in terms of the maximum of the dimension   of the local unstable manifolds of the isolated invariant sets, Lipschitz properties of the semigroup and the rate of exponential attraction. We also generalize this result for some special evolution processes, introducing a concept of Morse decomposition with pullback attractivity. Under suitable assumptions, if (A,A∗)(A,A∗) is an attractor–repeller pair for the attractor AA of a semigroup {T(t):t≥0}{T(t):t≥0}, then the fractal dimension of AA can be estimated in terms of the fractal dimension of the local unstable manifold of A∗A∗, the fractal dimension of AA, the Lipschitz properties of the semigroup and the rate of the exponential attraction. The ingredients of the proof are the notion of generalized gradient-like semigroups and their regular attractors, Morse decomposition and a fine analysis of the structure of the attractors. As we said previously, we generalize this result for some evolution processes using the same basic ideas.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 75, Issue 14, September 2012, Pages 5702–5722
نویسندگان
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