Metrical theory for $α$-Rosen fractions

Details Metrical theory for $α$-Rosen fractions Metrical theory for $α$-Rosen fractions

2007-02-18

arxiv.org/abs/math/0702516v2

Mathematics

Number Theory

Scientific paper

The Rosen fractions form an infinite family which generalizes the nearest-integer continued fractions. In this paper we introduce a new class of continued fractions related to the Rosen fractions, the $\alpha$-Rosen fractions. The metrical properties of these $\alpha$-Rosen fractions are studied. We find planar natural extensions for the associated interval maps, and show that these regions are closely related to similar region for the 'classical' Rosen fraction. This allows us to unify and generalize results of diophantine approximation from the literature.

Affiliated with

Also associated with

No associations

Rating

Metrical theory for $α$-Rosen fractions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Metrical theory for $α$-Rosen fractions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Metrical theory for $α$-Rosen fractions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-591491