18 citations · 30 across the 15 of their papers we have counts for
15 papers
Hausdorff Dimension of Growth Rate Level Sets in -expansions
Andreas Rusu, Gabriela Ileana Sebe
We investigate the Hausdorff dimension of level sets defined by digit growth rates in -expansions, a generalization of regular continued fractions. For any , we prove t…
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…
Hausdorff dimension of exceptional sets arising in -expansions
Gabriela Ileana Sebe, Dan Lascu
For a fixed , , let and be the -expansion of . Our first goal is to extend for -expansions the r…
On the -mixing coefficients of Rényi-type maps
Gabriela Ileana Sebe, Dan Lascu
Via dependence with complete connections we investigate the -mixing coefficients of the sequence of incomplete quotients and also of the doubly infini…
On the Extreme Value Behavior of -Expansions
Gabriela Ileana Sebe, Dan Lascu, Bilel Selmi
The main objective of this paper is to develop extreme value theory for -expansions. We establish the limit distribution of the maximum value in a -continued…
Some asymptotic results for the continued fraction expansions with odd partial quotients
Gabriela Ileana Sebe, Dan Lascu
We present and develop different approaches to study the asymptotic behavior of the distribution functions in the odd continued fractions case. Firstly, by considering the transiti…
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…
A dependence with complete connections approach to generalized Rényi continued fractions
Gabriela Ileana Sebe, Dan Lascu
We introduce and study in detail a special class of backward continued fractions that represents a generalization of Rényi continued fractions. We investigate the main metrical pro…
On convergence rate in the Gauss-Kuzmin problem for -expansions
Gabriela Ileana Sebe, Dan Lascu
After providing an overview of -expansions introduced by Chakraborty and Rao, we focus on the Gauss-Kuzmin problem for this new transformation. Actually, we complete our study o…
A two-dimensional Gauss-Kuzmin theorem for -continued fraction expansions
Gabriela Ileana Sebe, Dan Lascu
A two-dimensional Gauss-Kuzmin theorem for -continued fraction expansions is shown. More exactly, we obtain a Gauss-Kuzmin theorem related to the natural extension of the measur…
A gauss-kuzmin theorem and related questions for -expansions
Gabriela Ileana Sebe, Dan Lascu
Using the natural extension for -expansions, we give an infinite-order-chain representation of the sequence of the incomplete quotients of these expansions. Together with the er…