3 papers
math.DS2023
The extended Hausdorff dimension spectrum of a conformal iterated function system is maximal
Andrei E. Ghenciu, Ronnie Pavlov
For any conformal iterated function system (CIFS) consisting of finitely or countably many maps, and any closed shift-invariant set of right-infinite sequences of such maps, one ca…
math.DS2015
The Hausdorff dimension spectrum of Conformal Graph Directed Markov Systems and applications to Nearest Integer continued fractions
Andrei E. Ghenciu, Sara Munday, Mario Roy
In this paper, we consider two dynamical systems associated to the nearest integer continued fraction, and show that both of them have full Hausdorff dimension spectrum.
math.DS2007
Parabolic Iterated Function Systems with Applications to the Backward Continued Fractions
Andrei E. Ghenciu
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 Conje…