Real Analysis Exchange

Bowen’s Formula for Shift-Generated Finite Conformal Constructions

Andrei E. Ghenciu and Mario Roy

Full-text: Open access

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

Subjects
Primary: 28A78: Hausdorff and packing measures
Secondary: 28A80: Fractals [See also 37Fxx] 37B10: Symbolic dynamics [See also 37Cxx, 37Dxx]

Keywords
Hausdorff dimension pressure entropy

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


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