English

Phase Transitions of the Multifractal Spectrum

Dynamical Systems 2016-07-19 v1

Abstract

We consider the multifractal analysis of the pointwise dimension for Gibbs measures on countable Markov shifts. Our paper analyses the set of non-analytic points or phase transitions of the multifractal spectrum. By Sarig's thermodynamic formalism for countable Markov shifts and Iommi's expression of the multifractal spectrum, we apply analyticity arguments on the pressure function for the countable shift. Finally, we apply our results about the phase transitions of the multifractal spectrum to the Gauss map.

Keywords

Cite

@article{arxiv.1607.04786,
  title  = {Phase Transitions of the Multifractal Spectrum},
  author = {Jason Tomas Dungca},
  journal= {arXiv preprint arXiv:1607.04786},
  year   = {2016}
}