Record Details
Commensurable continued fractions
ScholarsArchive at Oregon State University
| Field | Value |
|---|---|
| Title | Commensurable continued fractions |
| Names |
Arnoux, Pierre
(creator) Schmidt, Thomas A. (creator) |
| Date Issued | 2014-11 (iso8601) |
| Note | This is the publisher’s final pdf. The published article is copyrighted by the American Institute of Mathematical Sciences and can be found at: http://aimsciences.org/journals/home.jsp?journalID=1. |
| 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. |
| Genre | Article |
| Topic | Continued fractions |
| Identifier | 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 |
