Pisot numbers and strong negations

Enrique de Amo, Manuel Díaz Carrillo and Juan Fernández-Sánchez

Chaos, Solitons & Fractals, 2017, vol. 104, issue C, 61-67

Abstract: We introduce and study representation systems for the numbers in the unit interval [0, 1]. We call them ϕm-systems (where ϕm is a pseudo-golden ratio). With the aid of these representation systems, we define a family hm of strong negations and an increasing function gm which is the inverse of the generator of hm. The functions hm and gm are singular, and we study several properties; among which we calculate the Hausdorff dimensions of certain sets that are related to them. Finally, we prove that gm is an infinite convolution, and the sequence of coefficients in the Fourier series of its associated Stieltjes measure does not converge to zero.

Keywords: Strong negation; Numbers representation system; Dynamical system; Ergodicity; Pisot number; Singular function; Fractal dimension; Fourier coefficients associated to a Stieltjes measure (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077917303211
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:104:y:2017:i:c:p:61-67

DOI: 10.1016/j.chaos.2017.08.002

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().