## Real Analysis Exchange

### Bowen’s Formula for Shift-Generated Finite Conformal Constructions

#### Abstract

We study shift-generated finite conformal constructions; i.e., conformal constructions generated by a general shift (shift of finite type, sofic shift and non-sofic shift alike) over a finite alphabet. These constructions are not restricted to shifts of finite type or sofic shifts as in the classical limit set constructions. In particular, we prove that the limit sets of such constructions satisfy Bowen’s formula, which gives the Hausdorff dimension of the limit set as the zero of the topological pressure. We look at several examples, including a one-dimensional construction generated by the so-called context-free shift.

#### Article information

Source
Real Anal. Exchange, Volume 40, Number 1 (2015), 99-112.

Dates
First available in Project Euclid: 1 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.rae/1435759197

Mathematical Reviews number (MathSciNet)
MR3365392

Zentralblatt MATH identifier
06848825

#### Citation

Ghenciu, Andrei E.; Roy, Mario. Bowen’s Formula for Shift-Generated Finite Conformal Constructions. Real Anal. Exchange 40 (2015), no. 1, 99--112. https://projecteuclid.org/euclid.rae/1435759197