Abstract:
An explicit construction of a reduced hyperbolic integer operator from the group $SL(2,\mathbb Z)$ 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 $SL(2,\mathbb Z)$ (which is based on Gauss' reduction theory) is experimentally studied.
Keywords:geometric continued fraction in the sense of Klein, period of a geometric continued fraction, hyperbolic integer operator, sail of an integer operator, LLS-sequence, integer length, integer sine.
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