Iteration of piecewise linear maps on an interval
JB Mcguire, CJ Thompson
Bulletin of the Australian Mathematical Society | Published : 1981
A complete analysis is given of the iterative properties of two piece-piecewise linear maps on an interval, from the point of view of a doubling transformation obtained by functional composition and rescaling. We show how invariant measures may be constructed for such maps and that parameter values where this may be done form a dense set in a one-dimensional subset of parameter space.