Geodesic
Remarks on the Fractal Dimension of Bi-Space Global and Exponential Attractors
Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 1, pp. 121-145

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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. 
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     title = {Remarks on the {Fractal} {Dimension} of {Bi-Space} {Global} and {Exponential} {Attractors}},
     journal = {Bollettino della Unione matematica italiana},
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Cholewa, Jan W.; Czaja, Radoslaw; Mola, Gianluca. Remarks on the Fractal Dimension of Bi-Space Global and Exponential Attractors. Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 1, pp. 121-145. http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_1_a5/