Symmetries of a two-dimensional continued fraction
- Authors: German O.N.1,2, Tlyustangelov I.A.1,2
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Affiliations:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Moscow Center for Fundamental and Applied Mathematics
- Issue: Vol 85, No 4 (2021)
- Pages: 53-68
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133847
- DOI: https://doi.org/10.4213/im9072
- ID: 133847
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Abstract
We describe the symmetry group of a multidimensional continued fraction. As a multidimensional generalization of continued fractions we consider Klein polyhedra. We distinguish two types of symmetries: Dirichlet symmetries, which correspond to the multiplication by units of the respective extension of $\mathbb{Q}$, and so-called palindromic symmetries. The main result is a criterion for a two-dimensional continued fraction to have palindromic symmetries, which is analogous to the well-known criterion for the continued fraction of a quadratic irrationality to have a symmetric period.
About the authors
Oleg Nikolaevich German
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Moscow Center for Fundamental and Applied Mathematics
Email: german.oleg@gmail.com
Doctor of physico-mathematical sciences, no status
Ibragim Aslanovich Tlyustangelov
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Moscow Center for Fundamental and Applied Mathematics
Email: ibragim-tls@yandex.ru
Candidate of physico-mathematical sciences, no status
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