Open Access
Translator Disclaimer
2013/2014 Bowen’s Formula for Shift-Generated Finite Conformal Constructions
Andrei E. Ghenciu, Mario Roy
Real Anal. Exchange 40(1): 99-112 (2013/2014).

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.

Citation

Download Citation

Andrei E. Ghenciu. Mario Roy. "Bowen’s Formula for Shift-Generated Finite Conformal Constructions." Real Anal. Exchange 40 (1) 99 - 112, 2013/2014.

Information

Published: 2013/2014
First available in Project Euclid: 1 July 2015

zbMATH: 06848825
MathSciNet: MR3365392

Subjects:
Primary: 28A78
Secondary: 28A80 , 37B10

Keywords: Entropy , Hausdorff dimension , pressure

Rights: Copyright © 2015 Michigan State University Press

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.40 • No. 1 • 2013/2014
Back to Top