9 papers · 1 filter
Sharp Hausdorff Dimension Bounds for Sets with Bounded and Growing Digits in -expansions
Andreea Catalina Chitu, Gabriela Ileana Sebe, Dan Lascu
We establish sharp bounds for the Hausdorff dimension of sets of irrational numbers in whose digits in the -expansion are either uniformly bounded or tend to infinity. F…
Limit Theorems for -expansions and the Failure of the Strong Law
Andreas Rusu, Gabriela Ileana Sebe, Dan Lascu
The paper presents fundamental metrical theorems for a class of continued fraction-like expansions known as -expansions. We first prove Khinchine's Weak Law of Large Numbers for…
A Lochs-Type Approach via Entropy in Comparing the Efficiency of Different Continued Fraction Algorithms
Dan Lascu, Gabriela Ileana Sebe
We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aimed t…
Two asymptotic distributions related to Rényi-type continued fraction expansions
Gabriela Ileana Sebe, Dan Lascu
We attempt to investigate a two-dimensional Gauss-Kuzmin theorem for Rényi-type continued fraction expansions. More precisely speaking, our focus is to obtain specific lower and up…
Convergence rate for Rényi-type continued fraction expansions
Gabriela Ileana Sebe, Dan Lascu
This paper continues our investigation of Renyi-type continued fractions studied in \cite{Sebe&Lascu-2018}. A Wirsing-type approach to the Perron-Frobenius operator of the Rényi-ty…
A Gauss-Kuzmin-Lévy theorem for Rényi-type continued fractions
Dan Lascu, Gabriela Ileana Sebe
We consider an interval map which is a generalization of the Rényi transformation. For the continued fraction expansion arising from this transformation, we prove a result concerni…