Project 04: "Fractal analysis and combinatorics of digital expansions"

This project is running since 2010.

Principal investigator: Peter Grabner
Graz University of Technology, Austria.
Mentor for: Alese, Zhang; Krenn, Minervino, Raseta.

DK Student

DK Student

  • First phase of the doctoral program:
  • Florian Greinecker (Austria; October 2010-April 2016)
    Email: greinecker@math.tugraz.at
    Mentors: Clemens Heuberger, Jörg Thuswaldner.

Associated Students

  • Second phase of the doctoral program:
  • Damir Ferizovic (Bosnia and Herzegovina; since December 2016)
    Email: damir.ferizovic@tugraz.at

Project description (pdf-file)

The proposer of this project has been interested in the analysis and probability on fractals since the early 1990s. He has written several publications on this subject, as well as supervised three related PhD-theses. He is especially interested in the application of generating function techniques to this subject, which gives a close relation to the iteration theory of rational functions. Furthermore, the proposer has contributed to the study of digital expansions and their probabilistic and ergodic properties. Especially, he is interested in the study of distribution properties of arithmetic functions related to digital expansions, such as additive and multiplicative functions and representation numbers for redundant numeration, application of techniques from ergodic theory and probability theory to the study of systems of numeration, and applications of redundant numeration to cryptography.