4 papers
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…
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.
Dynamical properties of S-gap shifts and other shift spaces
Simon Baker, Andrei E. Ghenciu
We study the dynamical properties of certain shift spaces. To help study these properties we introduce two new classes of shifts, namely boundedly supermultiplicative (BSM) shifts…
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…