Iterated Maps on the Interval as Dynamical Systems - Brossura

Collet, Pierre; Eckmann, J.-P.

Brossura

ISBN 10: 0817649301 ISBN 13: 9780817649302

Casa editrice: Birkhäuser, 2010

Riassunto

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.

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Review

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)

Dettagli dell?edizione

• Editore: Birkhäuser
• Data di pubblicazione: 2010
• ISBN 10: 0817649301
• ISBN 13: 9780817649302
• Rilegatura: Paperback
• Lingua: Inglese
• Numero di pagine: 262
• Contatto del produttore: non disponibile