Chaos on the interval - a survey of relationship between the various kinds of chaos for continuous interval maps

Dynamical systems on the interval were widely studied because they are among the simplest systems and nevertheless they turn out to have complex dynamics. Many works on chaos were inspired by the behaviour of interval maps. However these systems have many properties that are not found on other spaces. As a consequence, one-dimensional dynamics is very rich and worth a separate study. The aim of this book is to survey the relations between the various sorts of chaos and related notions for continuous interval maps. The papers on this topic are numerous but very scattered in the literature, sometimes little known or difficult to find; some were originally published only in Russian or without proof.Comment: Book (225 pages). Errata and changes between the published book and the arxiv version: see www.math.u-psud.fr/~ruette/abstracts/abstract-chaos-int.htm