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Dynamics of interval maps generated by erasing substitutions
- 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