Proper cyclic symmetries of multidimensional continued fractions

Abstract

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 algebraic continued fraction has proper cyclic palindromic symmetry in the case $n=4$. Klein polyhedra are considered as a multidimensional generalization of continued fractions.

arXiv comment24 pages, 7 figures In Russian