Nearest lambdaq-multiple fractions
Abstract
We discuss the nearest lambdaq--multiple continued fractions and their duals for lambdaq = 2 cos(pi/q) which are closely related to the Hecke triangle groups Gq, q=3,4,... . They have been introduced in the case q=3 by Hurwitz and for even q by Nakada. These continued fractions are generated by interval maps fq respectively fq* which are conjugate to subshifts over infinite alphabets. We generalize to arbitrary q a result of Hurwitz concerning the Gq-- and fq-equivalence of points on the real line. The natural extension of the maps fq and fq* can be used as a Poincare map for the geodesic flow on the Hecke surfaces Gq and allows to construct the transfer operator for this flow.
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