A Dual Approach to Triangle Sequences: A Multidimensional Continued Fraction Algorithm

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dc.creatorAssaf, S.
dc.creatorChen, L.
dc.creatorCheslack-Postava, T.
dc.creatorCooper, B.
dc.creatorDiesl, A.
dc.creatorGarrity, T.
dc.creatorLepinski, M.
dc.creatorSchuyler, A.
dc.date2002-06-10
dc.date.accessioned2026-07-07T04:49:02Z
dc.date.available2026-07-07T04:49:02Z
dc.descriptionA dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the triangle sequence. We give a new criterion for when a triangle sequence uniquely describes a pair of numbers and give the first explicit examples of triangle sequences that do not uniquely describe a pair of reals. Finally, this dual approach yields that the triangle sequence is topologically strongly mixing, meaning in particular that it is topologically ergodic.
dc.description58 pages, 15 figures
dc.identifierhttps://arxiv.org/abs/math/0206105
dc.identifierhttp://arxiv.org/abs/math/0206105
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64273
dc.subjectNumber Theory
dc.subject11J70, 11K50, 11A55
dc.titleA Dual Approach to Triangle Sequences: A Multidimensional Continued Fraction Algorithm
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