Abstract
An explicit construction of a reduced hyperbolic integer operator from the group SL(2, ℤ) such that one of the periods of the corresponding geometric continued fraction in the sense of Klein coincides with a given sequence of positive integers is presented. An algorithm determining periods for any operator in SL(2, ℤ) (which is based on Gauss’ reduction theory) is experimentally studied.
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Original Russian Text © O. N. Karpenkov, 2010, published in Matematicheskie Zametki, 2010, Vol. 88, No. 1, pp. 30–42.
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Karpenkov, O.N. Determination of periods of geometric continued fractions for two-dimensional algebraic hyperbolic operators. Math Notes 88, 28–38 (2010). https://doi.org/10.1134/S0001434610070035
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DOI: https://doi.org/10.1134/S0001434610070035