Iterated Maps on the Interval as Dynamical Systems

• Motivation and Interpretation.- One-Parameter Families of Maps.- Typical Behavior for One Map.- Parameter Dependence.- Systematics of the Stable Periods.- On the Relative Frequency of Periodic and Aperiodic Behavior.- Scaling and Related Predictions.- Higher Dimensional Systems.- Properties of Individual Maps.- Unimodal Maps and Thier Itineraries.- The Calculus of Itineraries.- Itineraries and Orbits.- Negative Schwarzian Derivative.- Homtervals.- Topological Conjugacy.- Sensitive Dependence on Initial Conditions.- Ergodic Properties.- Properties of one-Parameter families of maps.- One-Parameter Families of Maps.- Abundance of Aperiodic Behavior.- Universal Scaling.- Multidimensional Maps.

From the reviews: This book is a thorough and readable introduction to some aspects of the theory of one-dimensional dynamical systems...The kneading calculus of Milnor-Thurston receives its most accessible treatment to date in print...This is an important and beautiful exposition, both as an orientation for the reader unfamiliar with this theory and as a prelude to studying in greater depth some of the hard papers on the subject. -Mathematical Reviews (Review of the original hardcover edition) This book provides a good survey of recent developments in the study of the dynamics of smooth self-maps on the interval. It...deals with a subject whose literature often appears in physics journals. This literature suffers in general from a failure to distinguish between mathematical theorems and 'facts' determined empirically, usually by computer experiment. It is a difficult task to consider both of these types of information and carefully maintain the distinction (an absolute necessity from the point of view of a mathematician). The work under review seems to do a good job of this...On the whole this work is a good one meeting a need to survey recent results in this active and important area of mathematics. -Zentralblatt MATH (Review of the original hardcover edition) "This book is essentially a reprint of the influential and classic 1980 Edition ... in the area of one-dimensional dynamics for maps of the interval. ... make a positive addition to this vital milestone work in the field of dynamical systems." (Steve Pederson, Zentralblatt MATH, Vol. 1192, 2010)