Frequency of digits in the Luroth expansion
Date
2009
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Abstract
In 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.
Description
Keywords
Frequency of digits, Luroth expansion, COUNTABLE MARKOV SHIFTS, MULTIFRACTAL ANALYSIS