English

Quantization dimension for infinite conformal iterated function systems

Dynamical Systems 2018-11-02 v1

Abstract

The quantization dimension function for an FF-conformal measure mFm_F generated by an infinite conformal iterated function system satisfying the strong open set condition and by a summable H\"{o}lder family of functions is expressed by a simple formula involving the temperature function of the system. The temperature function is commonly used to perform the multifractal analysis, in our context of the measure mFm_F. The result in this paper extends a similar result of Lindsay and Mauldin established for finite conformal iterated function systems [Nonlinearity 15 (2002)].

Keywords

Cite

@article{arxiv.1811.00299,
  title  = {Quantization dimension for infinite conformal iterated function systems},
  author = {Jason Atnip and Mrinal Kanti Roychowdhury and Mariusz Urbański},
  journal= {arXiv preprint arXiv:1811.00299},
  year   = {2018}
}