Parabolic Iterated Function Systems with Applications to the Backward Continued Fractions

2007/11/08 by Andrei E. Ghenciu, Ghenciu, Andrei E.
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.0711.1336

arxiv created 2007/11/08 · arxiv updated 2009/12/01

Abstract

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 in1] there exists a subsystem whose limit set has Hausdorff dimension t

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