Zobrazeno 1 - 10
of 82
pro vyhledávání: '"Kalle, Charlene"'
A continued fraction algorithm allows to represent numbers in a way that is particularly valuable if one wants to approximate irrational numbers by rationals. Some of these algorithms are simple in the sense that the possible representations can be c
Externí odkaz:
http://arxiv.org/abs/2406.18689
Autor:
Boonstra, Aafko, Kalle, Charlene
Let $L=(L_d)_{d \in \mathbb N}$ be any ordered probability sequence, i.e., satisfying $0 < L_{d+1} \le L_d$ for each $d \in \mathbb N$ and $\sum_{d \in \mathbb N} L_d =1$. We construct sequences $A = (a_i)_{i \in \mathbb N}$ on the countably infinite
Externí odkaz:
http://arxiv.org/abs/2402.14500
In this article we study Besicovitch-Eggleston sets for finite GLS number systems with redundancy. These number systems produce number expansions reminiscent of Cantor base expansions. The redundancy refers to the fact that each number $x \in [0,1]$
Externí odkaz:
http://arxiv.org/abs/2310.15265
Autor:
Huang, Yan, Kalle, Charlene
For a fixed $\alpha$, each real number $x \in (0,1)$ can be represented by many different generalised $\alpha$-L\"uroth expansions. Each such expansion produces for the number $x$ a sequence of rational approximations $(\frac{p_n}{q_n})_{n \ge 1}$. I
Externí odkaz:
http://arxiv.org/abs/2306.12114
The $\beta$-encoder is an analog circuit that converts an input signal $x \in [0,1]$ into a finite bit stream $\{b_i\}$. The bits $\{b_i\}$ are correlated and therefore are not immediately suitable for random number generation, but they can be used t
Externí odkaz:
http://arxiv.org/abs/2303.13170
We first survey the current state of the art concerning the dynamical properties of multidimensional continued fraction algorithms defined dynamically as piecewise fractional maps and compare them with algorithms based on lattice reduction. We discus
Externí odkaz:
http://arxiv.org/abs/2303.07777
Autor:
Homburg, Ale Jan, Kalle, Charlene
We analyze the two-point motions of iterated function systems on the unit interval generated by expanding and contracting affine maps, where the expansion and contraction rates are determined by a pair $(M,N)$ of integers. This dynamics depends on th
Externí odkaz:
http://arxiv.org/abs/2207.09987
Autor:
Kalle, Charlene, Zeegers, Benthen
For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending on the ran
Externí odkaz:
http://arxiv.org/abs/2206.07601
In 1964 Lochs proved a theorem on the number of continued fraction digits of a real number $x$ that can be determined from just knowing its first $n$ decimal digits. In 2001 this result was generalised to a dynamical systems setting by Dajani and Fie
Externí odkaz:
http://arxiv.org/abs/2110.14466
We continue the study of random continued fraction expansions, generated by random application of the Gauss and the R\'enyi backward continued fraction maps. We show that this random dynamical system admits a unique absolutely continuous invariant me
Externí odkaz:
http://arxiv.org/abs/2110.05786