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

作者：Schweiger F^*

来源：International Journal of Number Theory, 2012, 8(1): 149-160.

DOI：10.1142/S179304211250008X

• Multidimensional continued fractions
• ergodic theory

Moshchevitin and Vielhaber gave an interesting generalization of the Farey-Brocot sequence for dimension d %26gt;= 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 A and algorithm B. Algorithm B is related to a proposal of Monkemeyer and to Selmer algorithm (see [G. Panti, Multidimensional continued fractions and a Minkowski function, Monatsh. Math. 154 (2008) 247-264]). However, algorithm A 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.

• 出版日期2012-2