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Article overview
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Exponential growth of norms in semigroups of linear automorphisms and Hausdorff dimension of self-projective IFS | Roberto De Leo
; | Date: |
1 Apr 2012 | Abstract: | Given a finitely generated semigroup S of the (normed) set of linear maps of
a vector space V into itself, we find sufficient conditions for the exponential
growth of the number N(k) of elements of the semigroup contained in the sphere
of radius k as k->infinity. We relate the growth rate lim log N(k)/log k to the
exponent of a zeta function naturally defined on the semigroup and, in case S
is a semigroup of volume-preserving automorpisms, to the Hausdorff and box
dimensions of the limit set of the induced semigroup of automorphisms on the
corresponding projective space. | Source: | arXiv, 1204.0250 | Services: | Forum | Review | PDF | Favorites |
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