Dynamical Systems for U-Maps

Abstract

When considering one-dimensional dynamical systems, it is convenient to begin with the investigation of the so-called unimodal maps, because they are (in a certain sense) the simplest ones. A map f ∈ C⁰(I, I) is called unimodal if the interval I can be decomposed into the intervals I₁ and I₂ so that the map f is a homeomorphism both on I₁ and I₂, and moreover, it monotonically increases on one of these intervals and monotonically decreases on the other one (this decomposition, clearly, depends of f).