Can I read Exponential growth of norms in semigroups of linear automorphisms and Hausdorff dimension of self-projective IFS on EtoBox?

Exponential growth of norms in semigroups of linear automorphisms and Hausdorff dimension of self-projective IFS by De Leo, Roberto is a scholarly article available to read on EtoBox.

What is Exponential growth of norms in semigroups of linear automorphisms and Hausdorff dimension of self-projective IFS about?

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.

Author

De Leo, Roberto

Published

2012

Language

EN