Geodesic
The dimension of attractors of $k$-contracting systems in an infinite-dimensional space
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1983), pp. 52-59

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An upper estimate is given for the Hausdorff dimension of attractors of non-linear semigroups in Hilbert space, the transformations of the semigroup are contracting $k$-dimensional volumes. It is proved that this dimension does not exceed $k$. 
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     author = {Yu. S. Ilyashenko},
     title = {The dimension of attractors of $k$-contracting systems in an infinite-dimensional space},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {52--59},
     publisher = {mathdoc},
     number = {3},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a9/}
}
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Yu. S. Ilyashenko. The dimension of attractors of $k$-contracting systems in an infinite-dimensional space. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1983), pp. 52-59. http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a9/