On periodic orbits of trapezoid maps (Q1261856)

A trapezoid map on the unit interval is defined as follows: \(f(x) = ax\), for \(0 \leq x \leq b\), \(f(x) = ab\), for \(b\leq x \leq 1-b\), \(f(x) = a(1- x)\), for \(1-b \leq x \leq 1\), where \(a\), \(b\) are suitable parameters. For such maps: (1) Stable periodic orbits are characterized in terms of the kneading theory, (2) Regions of parameters where the maps have stable periodic orbits are determined.