Digitale Medien
Springer
Journal of dynamics and differential equations
11 (1999), S. 557-581
ISSN:
1572-9222
Schlagwort(e):
Global attractors
;
inertial manifolds
;
exponential attractors
;
connectedness
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract Many dissipative evolution equations possess a global attractor $$A$$ with finite Hausdorff dimension d. In this paper it is shown that there is an embedding X of $$A$$ into $$\mathbb{R}^N $$ , with N=[2d+2], such that X is the global attractor of some finite-dimensional system on $$\mathbb{R}^N $$ with trivial dynamics on X. This allows the construction of a discrete dynamical system on $$\mathbb{R}^N $$ which reproduces the dynamics of the time T map on $$A$$ and has an attractor within an arbitrarily small neighborhood of X. If the Hausdorff dimension is replaced by the fractal dimension, a similar construction can be shown to hold good even if one restricts to orthogonal projections rather than arbitrary embeddings.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1023/A:1021918004832
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