On the scaling properties of the period-increment scenario in dynamical systems
Period doubling scenarios, or more general period-multiplying scenarios are widely known, and universal scaling constants have been found, e.g., for unimodal maps. An arithmetic sequence of periods occurs in period increment scenarios, where in each bifurcation the number of periodic orbits changes by an additive constant. In this paper, the authors give two very simple examples of discontinuous maps of an interval that exhibit the latter behaviour, and for which bifurcation points and scaling constants can be computed analytically. However, these constants are not universal in the second example; they depend on the parameters.
scientific article; zbMATH DE number 1501100