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. The diagram below names the main notions we will consider and sums up the links between them.

summary diagram

published book: Chaos on the interval. Volume 67 of University Lecture Series, AMS, 2017.

pdf version (last revision April 12, 2018): [arXiv:1504.03001] [pdf]

Errata and changes between the published book and the pdf version

Since there are additional citations, this shifts the numbers in the bibliography.