Leírás
Abstract: In the last four decades, considerable attention has been
given to self-similar Iterated Function Systems (IFS). In this talk, we
consider a more general family of IFSs on the line. Namely, systems
consisting of continuous piecewise linear functions whose slopes are
different from zero and smaller than one in absolute value. We call
these systems Continuous Piecewise Linear Iterated Function Systems
(CPLIFS). A celebrated result of M. Hochman shows that the Hausdorff
dimension of the attractor of a typical self-similar IFS on the line is
equal to the minimum of one and the similarity dimension of the IFS. As
a generalization of this result, I will show that the Hausdorff
dimension of the attractor of a typical CPLIFS is equal to the minimum
of one and the exponent obtained from the most natural system of covers
of the attractor. The new results presented are joint with Peter Raith
and Károly Simon.