Abstract
In a recent work, we proved that under natural conditions satisfied in several important examples, the rate of growth 1/sA of norms of matrices in a semigroup (respectively ) dictates the Hausdorff dimension of the attractor RA of the corresponding semigroups of projective transformations on (respectively ). In the present work, we begin a study of the higher-dimensional case. In particular, we introduce a certain family of semigroups , and we study numerically concrete cases for n = 3 and n = 4. Our results suggest that for n ≥ 3, (n − 1)sA/n is a lower bound for the Hausdorff dimension of RA.
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