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Dynamics of interval maps generated by erasing substitutions

Authors :
A. Della Corte
M. Farotti
Source :
Journal of Differential Equations. 323:86-112
Publication Year :
2022
Publisher :
Elsevier BV, 2022.

Abstract

We study discontinuous interval maps generated by the action of erasing block substitutions on the binary expansion. After establishing some general properties of these maps, we categorize erasing block substitutions in a hierarchy of classes displaying progressively stronger erasing character. We investigate how this affects the dynamics of the corresponding interval maps, showing that the richest dynamical behavior (Devaney and Li-Yorke chaos, infinite topological entropy) is achieved at a precise step in this hierarchy, which we name completely erasing substitutions. KEYWORDS: Topological dynamics, Erasing substitutions; Devaney chaos; Li-Yorke chaos; Topological entropy.<br />28 pages

Details

ISSN :
00220396
Volume :
323
Database :
OpenAIRE
Journal :
Journal of Differential Equations
Accession number :
edsair.doi.dedup.....64ccec2d40732ff86de22bceb41f98df
Full Text :
https://doi.org/10.1016/j.jde.2022.03.036