Inverse limits on [0,1] using sequences of piecewise linear unimodal bonding maps (Q1862048)

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.