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Periodicity of general multidimensional continued fractions using repetend matrix form

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Publication:6510881

DOI10.1016/J.EXMATH.2024.125571arXiv2307.00898MaRDI QIDQ6510881

Author name not available (Why is that?)


Abstract: 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.





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