Browsing by Author "Barreira, Luis"
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- ItemFrequency of digits in the Luroth expansion(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2009) Barreira, Luis; Iommi, GodofredoIn this note we consider the Luroth expansion of a real number, and we Study the Hausdorff dimension of a class of sets defined in terms of the frequencies of digits in the expansion. We also study the speed at which the approximants obtained from the Luroth expansion converge. In addition, we describe the multifractal properties of the level sets of the Lyapunov exponent, which measures the exponential speed of approximation obtained from the approximants. Finally, we describe the relation of the Luroth expansion with the continued fraction expansion and the beta-expansion. We remark that our work is still another application of the theory of dynamical systems to number theory. (C) 2008 Elsevier Inc. All rights reserved.
- ItemPartial quotients of continued fractions and beta-expansions(IOP PUBLISHING LTD, 2008) Barreira, Luis; Iommi, GodofredoFor each real number, we obtain an asymptotic for the number of partial quotients in the continued fraction expansion that can be obtained from the first n terms of its beta-expansion. A novelty of our approach is the use of methods of the theory of dynamical systems.