2009/02/23 by Dieter Mayer, Mayer, Dieter, Tobias Mühlenbruch +1
Mathematics · #11A55 (Primary) 11J70 #30B70 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT #msc:11A55 #msc:11J70 #msc:30B70
paper · pdf · doi:10.48550/arxiv.0902.3953
46 pages, some typos corrected
arxiv created 2010/04/26 · arxiv updated 2010/04/27
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\H and allows to construct the transfer operator for this flow.