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Commensurable continued fractions Public Deposited

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  • 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.
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  • 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
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  • The first named-author gratefully acknowledges support through the ANR project SubTile.
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  • description.provenance : Made available in DSpace on 2014-07-16T16:00:24Z (GMT). No. of bitstreams: 1 SchmidtThomasMathematicsCommensurableContinuedFractions.pdf: 3955500 bytes, checksum: 214069cbdd95cdc95092134d2a0f0d26 (MD5) Previous issue date: 2014-11
  • description.provenance : Approved for entry into archive by Erin Clark(erin.clark@oregonstate.edu) on 2014-07-16T16:00:24Z (GMT) No. of bitstreams: 1 SchmidtThomasMathematicsCommensurableContinuedFractions.pdf: 3955500 bytes, checksum: 214069cbdd95cdc95092134d2a0f0d26 (MD5)
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