scholarly journals The derivative of the Minkowski function

2021 ◽  
Vol 85 (5) ◽  
Author(s):  
Dmitrii Radislavovich Gaifulin ◽  
Igor' Davidovich Kan
Keyword(s):  
Minkowski Function

A 2-DIMENSIONAL ALGORITHM RELATED TO THE FAREY–BROCOT SEQUENCE

2012 ◽  
Vol 08 (01) ◽  
pp. 149-160
Author(s):  
F. SCHWEIGER
Keyword(s):  
Continued Fractions ◽  
Dual Algorithm ◽  
Ergodic Properties ◽  
Minkowski Function ◽  
Special Cases ◽  
Multidimensional Continued Fractions ◽  
New Type ◽  
Interesting Generalization

Moshchevitin and Vielhaber gave an interesting generalization of the Farey–Brocot sequence for dimension d ≥ 2 (see [N. Moshchevitin and M. Vielhaber, Moments for generalized Farey–Brocot partitions, Funct. Approx. Comment. Math.38 (2008), part 2, 131–157]). For dimension d = 2 they investigate two special cases called algorithm [Formula: see text] and algorithm [Formula: see text]. Algorithm [Formula: see text] is related to a proposal of Mönkemeyer and to Selmer algorithm (see [G. Panti, Multidimensional continued fractions and a Minkowski function, Monatsh. Math.154 (2008) 247–264]). However, algorithm [Formula: see text] seems to be related to a new type of 2-dimensional continued fractions. The content of this paper is first to describe such an algorithm and to give some of its ergodic properties. In the second part the dual algorithm is considered which behaves similar to the Parry–Daniels map.

scholarly journals The Minkowski function and Salemʼs problem

2012 ◽  
Vol 350 (3-4) ◽  
pp. 137-140 ◽  
Author(s):  
Giedrius Alkauskas
Keyword(s):  
Minkowski Function

Differentiability of the Minkowski function $?(x)$. II

2019 ◽  
Vol 83 (5) ◽  
pp. 957-989
Author(s):  
I. D. Kan
Keyword(s):  
Minkowski Function
Sign in / Sign up

Export Citation Format

Share Document