PARABOLIC ITERATED FUNCTION SYSTEMS WITH APPLICATIONS TO THE BACKWARD CONTINUED FRACTIONS
Andrei E. Ghenciu · Far East Journal of Dynamical Systems · 2007
To the Renyi or backward continued fraction transformation we associate a parabolic iterated function system whose limit set has Hausdorff dimension 1. We show that the Texan Conjecture holds, i.e., for every t∈[0, 1] there exists a subsystem whose limit set has Hausdorff dimension t.