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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.

Determination of periods of geometric continued fractions for two-dimensional algebraic hyperbolic operators