Periodicity of general multidimensional continued fractions using repetend matrix form
| Autor: | Řada, Hanka, Starosta, Štěpán, Kala, Vítězslav |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Expo. Math. 42 (2024), article 125571, 36 pp |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.exmath.2024.125571 |
| Popis: | We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend, and use it to prove that a number of vectors has an eventually periodic expansion in the Algebraic Jacobi--Perron Algorithm. Further, we give criteria for vectors to have purely periodic expansions; in particular, the vector cannot be totally positive. Comment: 31 pages |
| Databáze: | arXiv |
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