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Hausdorff dimension estimation for attractors of nonautonomous dynamical systems in unbounded domains: An example
Author(s) -
Chepyzhov V. V.,
Efendiev M. A.
Publication year - 2000
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(200005)53:5<647::aid-cpa5>3.0.co;2-#
Subject(s) - mathematics , hausdorff dimension , attractor , hausdorff space , dynamical systems theory , dimension (graph theory) , pure mathematics , mathematical analysis , physics , quantum mechanics
The subject of this paper is the asymptotic behavior of a class of nonautonomous, infinite‐dimensional dynamical systems with an underlying unbounded domain. We present an approach that is able to overcome both the law of compactness of the trajectories and the continuity of the spectrum of the linear part of the equations under consideration, providing nevertheless existence of uniform attractors. Moreover, our approach allows us to estimate the Hausdorff dimension of attractors of nonautonomous equations in terms of physical parameters. © 2000 John Wiley & Sons, Inc.