Inverse limits on [0,1] using sequences of piecewise linear unimodal bonding maps
type: Item
instance of: scholarly article
title: Inverse limits on [0,1] using sequences of piecewise linear unimodal bonding maps
zbMATH Open document ID: 1014.37029
DOI: 10.1016/S0166-8641(01)00245-0
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: This paper deals with the dynamical properties of the two-parameter family \({\mathfrak A}=\{g_{b,c}\mid 0\leq b\leq 1,\;0<c<1\}\) defined by \[ g_{b,c}=\begin{cases} \frac{1-b}{c} x+b & \text{if }x\leq c,\\ \frac {1-x}{1-c} & \text{if }x\geq c.\end{cases}\tag{1} \] The family of functions, \(\mathfrak A\), contains some families which are quite important in their own right, in particular the full tent map. Here the author is interested in the limits of sequences of functions from the family \(\mathfrak A\). Much is known about the dynamics and inverse limit spaces that these functions induce when used as a single map, but virtually nothing is known when one considers a sequence of these functions.
Mathematics Subject Classification ID: 37E05
Mathematics Subject Classification ID: 37B45
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 54F15
zbMATH DE Number: 1879090
zbMATH Keywords: inverse limit
zbMATH Keywords: unimodal
zbMATH Keywords: continuum
zbMATH Keywords: indecomposable
zbMATH Keywords: two-parameter family of map
zbMATH Keywords: unimodal map
author: Brian E. Raines
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Some applications of an approximation theorem for inverse limits
cites work: Q4004856
cites work: Periodicity and Indecomposability
cites work: Q4512386
cites work: Inverse limits on $[0,1]$ using piecewise linear unimodal bonding maps
cites work: Q4004123
full work available at URL: s0166-8641(01)00245-0
OpenAlex ID: W2012804995
description: scientific article; zbMATH DE number 1879090