Explicit renormalisation in piecewise linear bimodal maps

Abstract

We discuss 2 two-parameter families of piecewise linear bimodal (two-hump) maps. The first example arises naturally in the study of bimodal maps: any bimodal map is semi-conjugate to a member of this family and topological entropy is preserved. The second example is a symmetric subcase of a map derived from a simple pulse-modulated feedback system. In each case we define an explicit map of parameter space which governs the effect of renormalisation, and use it to describe the non-wandering set.