Quadratic regular reversal maps
This paper studies how one-parameter families of unimodal maps depend on the parameter, for example when period doubling holds and when it disappears. Several examples are given where a perturbation may or may not destroy the chaotic behavior. To do this the authors introduce the notion of regular reversal map. In studying quadratic regular reversal maps, the authors find sufficient conditions for a map to only have periodic points with periods being powers of 2. The examples show that by considering families of regular reversal maps, it is straightforward to construct specific bifurcation diagrams with or without chaos.
scientific article; zbMATH DE number 2160818