An arithmetic group associated with a Pisot unit, and its symbolic-dynamical representation
Ergodic Properties of the Erdös Measure, the Entropy of the Goldenshift, and Related Problems.
On the topology of sums in powers of an algebraic number
Multidimensional self-affine sets: non-empty interior and the set of uniqueness
Let M be a d × d real contracting matrix. We consider the self-affine iterated function system Mv-u, Mv+u, where u is a cyclic vector. Our main result is as follows: if , then the attractor has non-empty interior. We also consider the set of points in which have a unique address. We show that unless M belongs to a very special (non-generic) class, the Hausdorff dimension of is positive. For this special class the full description of is given as well. This paper continues our work begun...
On a devil’s staircase associated to the joint spectral radii of a family of pairs of matrices
The joint spectral radius of a finite set of real matrices is defined to be the maximum possible exponential rate of growth of products of matrices drawn from that set. In previous work with K. G. Hare and J. Theys we showed that for a certain one-parameter family of pairs of matrices, this maximum possible rate of growth is attained along Sturmian sequences with a certain characteristic ratio which depends continuously upon the parameter. In this note we answer some open questions from that paper...
Number of representations related to a linear recurrent basis
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