Bi-space global and exponential attractors for the time continuous dynamical systems are considered and the bounds on their fractal dimension are discussed in the context of the smoothing properties of the system between appropriately chosen function spaces. The case when the system exhibits merely some partial smoothing properties is also considered and applications to the sample problems are given.
In questo lavoro sono considerate le nozioni di attrattori globali ed esponenziali "bi-space" per sistemi dinamici continui, e discusse limitazioni relative alla loro dimensione frattale in spazi di funzioni opportuni. Di particolare interesse è il caso in cui il sistema presenta un parziale effetto regolarizzante, ed alcuni esempi con questa proprietà sono mostrati.
@article{BUMI_2008_9_1_1_121_0,
author = {Jan W. Cholewa and Radoslaw Czaja and Gianluca Mola},
title = {Remarks on the Fractal Dimension of Bi-Space Global and Exponential Attractors},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {1},
year = {2008},
pages = {121-145},
zbl = {1213.37111},
mrnumber = {2388001},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2008_9_1_1_121_0}
}
Cholewa, Jan W.; Czaja, Radoslaw; Mola, Gianluca. Remarks on the Fractal Dimension of Bi-Space Global and Exponential Attractors. Bollettino dell'Unione Matematica Italiana, Tome 1 (2008) pp. 121-145. http://gdmltest.u-ga.fr/item/BUMI_2008_9_1_1_121_0/
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