Non-normal numbers in dynamical systems fulfilling the specification property
Year: 2014
Type: preprint
Abstract: In the present paper we want to focus on this dichotomy of the non-normal numbers -- on the one hand they are a set of measure zero and on the other hand they are residual -- for dynamical system fulfilling the specification property. These dynamical systems are motivated by $β$-expansions. We consider the limiting frequencies of digits in the words of the languagse arising from these dynamical systems, and show that not only a typical $x$ in the sense of Baire is non-normal, but also its Cesàro variants diverge.
Source: arXiv (Cornell University)
Institutions: Université Joseph Fourier, Institut Fourier
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951129790