5 citations · 5 across the 5 of their papers we have counts for
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On symmetries of 3-dimensional algebraic continued fractions
Ibragim A. Tlyustangelov
In this paper we prove in detail a criterion for an algebraic continued fraction to have a proper palindromic symmetry in dimension . We also present a new proof of the criterio…
Proper symmetries of 3-dimensional continued fractions
I. A. Tlyustangelov
In this work we prove a criterion for an algebraic continued fraction to have a proper palindromic symmetry in dimension . As a multidimensional generalization of continued frac…
Proper cyclic symmetries of multidimensional continued fractions
Ibragim A. Tlyustangelov
This work is devoted to the proof of the statement about the existence of palindromic continued fractions in an arbitrary dimension. In addition, it is proved the criterion that an…
Symmetries of a two-dimensional continued fraction
Oleg N. German, Ibragim A. Tlyustangelov
In this paper we describe the group of symmetries of a two-dimensional continued fraction. As a multidimensional generalization of continued fractions we consider Klein polyhedra.…
Palindromes and periodic continued fractions
Oleg N. German, Ibragim A. Tlyustangelov
This paper is devoted to a detailed exposition of geometry of continued fractions. We pay particular interest to the case of quadratic irrationalities and use the technique describ…