Commensurable continued fractions

Citeable URL: https://ir.library.oregonstate.edu/concern/articles/zw12z701p

Descriptions

Attribute Name	Values
Creator	Arnoux, Pierre Schmidt, Thomas A.
Abstract	We compare two families of continued fractions algorithms, the symmetrized Rosen algorithm and the Veech algorithm. Each of these algorithms expands real numbers in terms of certain algebraic integers. We give explicit models of the natural extension of the maps associated with these algorithms; prove that these natural extensions are in fact conjugate to the first return map of the geodesic flow on a related surface; and, deduce that, up to a conjugacy, almost every real number has an infinite number of common approximants for both algorithms. Keywords: Fuchsian groups, Geodesic flow, Natural extension, Continued fractions, Moebius transformations
Resource Type	Article
DOI	https://doi.org/10.3934/dcds.2014.34.4389
Date Available	2014-07-16T16:00:24+00:00
Date Issued	2014-11
Citation	Arnoux, P., & Schmidt, T. A. (2014). Commensurable continued fractions. Discrete and Continuous Dynamical Systems, 34(11), 4389-4418. doi:10.3934/dcds.2014.34.4389
Journal Title	Discrete and Continuous Dynamical Systems
Journal Volume	34
Journal Issue/Number	11
Urheberrechts-Erklärung	Copyright Not Evaluated
Publisher	American Institute of Mathematical Sciences
Peer Reviewed	Yes
Language	English [eng]
Replaces	http://hdl.handle.net/1957/50460