5 papers
On finite -expansions for the set of natural numbers
Túlio O. Carvalho, Catharina M. Moreira
We present a study of the problem of finiteness of the -expansions for the set of natural numbers, condition in brief, for three families of Pisot numbers for which the $β…
Spectral Hausdorff dimensions for a class of Schrödinger operators in bounded intervals
Vanderléa R. Bazao, Túlio O. Carvalho, César R. de Oliveira
Exact Hausdorff dimensions are computed for singular continuous components of the spectral measures of a class of Schrödinger operators in bounded intervals.
Lower bounds for fractal dimensions of spectral measures of the period doubling Schrödinger operator
Vanderlea R. Bazao, Tulio O. Carvalho, Cesar R. de Oliveira
It is shown that there exits a lower bound to the Hausdorff dimension of the spectral measures of the one-dimensional period doubling substitution Schrödinger operator, and,…
Study of the transcendence of a family of generalized continued fractions
Túlio O. Carvalho
We study a family of generalized continued fractions, which are defined by a pair of substitution sequences in a finite alphabet. We prove that they are stammering sequences, in th…
Hybrid Quasicrystals, Transport and Localization in Products of Minimal Sets
Tulio O. Carvalho, Cesar R. de Oliveira
We consider convex combinations of finite-valued almost periodic sequences (mainly substitution sequences) and put them as potentials of one-dimensional tight-binding models. We pr…