Iterated Maps on the Interval as Dynamical Systems PDF Download
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Author: Pierre Collet
Publisher:
ISBN:
Category :
Languages : en
Pages : 248
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Book Description
Author: Pierre Collet
Publisher:
ISBN:
Category :
Languages : en
Pages : 248
Get Book Here
Book Description
Author: Pierre Collet
Publisher: Springer Science & Business Media
ISBN: 0817649271
Category : Science
Languages : en
Pages : 259
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Book Description
Iterations of continuous maps of an interval to itself serve as the simplest examples of models for dynamical systems. These models present an interesting mathematical structure going far beyond the simple equilibrium solutions one might expect. If, in addition, the dynamical system depends on an experimentally controllable parameter, there is a corresponding mathematical structure revealing a great deal about interrelations between the behavior for different parameter values. This work explains some of the early results of this theory to mathematicians and theoretical physicists, with the additional hope of stimulating experimentalists to look for more of these general phenomena of beautiful regularity, which oftentimes seem to appear near the much less understood chaotic systems. Although continuous maps of an interval to itself seem to have been first introduced to model biological systems, they can be found as models in most natural sciences as well as economics. Iterated Maps on the Interval as Dynamical Systems is a classic reference used widely by researchers and graduate students in mathematics and physics, opening up some new perspectives on the study of dynamical systems .
Author: Alexander S. Mikhailov
Publisher: Springer Science & Business Media
ISBN: 364280196X
Category : Computers
Languages : en
Pages : 284
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Book Description
The second edition of this volume has been extensively revised. A different version of Chap. 7, reflecting recent significant progress in understanding of spatiotempo ral chaos, is now provided. Much new material has been included in the sections dealing with intermittency in birth-death models and noise-induced phase transi tions. A new section on control of chaotic behavior has been added to Chap. 6. The subtitle of the volume has been changed to better reflect its contents. We acknowledge stimulating discussions with H. Haken and E. Scholl and are grateful to our colleagues M. Bar, D. Battogtokh, M. Eiswirth, M. Hildebrand, K. Krischer, and V. Tereshko for their comments and assistance. We thank M. Lubke for her help in producing new figures for this volume. Berlin and Moscow A. s. Mikhailov April 1996 A. Yu. Loskutov Preface to the First Edition This textbook is based on a lecture course in synergetics given at the University of Moscow. In this second of two volumes, we discuss the emergence and properties of complex chaotic patterns in distributed active systems. Such patterns can be produced autonomously by a system, or can result from selective amplification of fluctuations caused by external weak noise.
Author: Hans Jürgen Korsch
Publisher: Springer Science & Business Media
ISBN: 3662038668
Category : Science
Languages : en
Pages : 327
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Book Description
Chaos: A Program Collection for the PC presents an outstanding selection of executable programs with introductory texts to chaos theory and its simulation. Students in physics, mathematics, and engineering will find a thorough introduction to fundamentals and applications in this field. Many numerical experiments and suggestions for further studies help the reader to become familiar with this fascinating topic. The second edition includes one CD-ROM, the executable programs are Windows 95 compatible.
Author: Saber N Elaydi
Publisher: World Scientific
ISBN: 9814466654
Category : Mathematics
Languages : en
Pages : 438
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Book Description
This volume holds a collection of articles based on the talks presented at ICDEA 2007 in Lisbon, Portugal.The volume encompasses current topics on stability and bifurcation, chaos, mathematical biology, iteration theory, nonautonomous systems, and stochastic dynamical systems.
Author: Luis Alseda
Publisher: World Scientific
ISBN: 9814548308
Category :
Languages : en
Pages : 188
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Book Description
These proceedings contain a collection of papers on Combinatorial Dynamics, from the lectures that took place during the international symposium, Thirty Years after Sharkovskiĭ's Theorem: New Perspectives, which was held at La Manga del Mar Menor, Murcia, Spain, from June 13 to June 18, 1994.Since Professor A N Sharkovskiĭ's landmark paper on the coexistence of periods for interval maps, several lines of research have been developed, opening applications of models to help understand a number of phenomena from a wide variety of fields, such as biology, economics, physics, etc. The meeting served to summarize the progress made since Professor Sharkovskiĭ's discovery, and to explore new directions.
Author: Jim M Cushing
Publisher: World Scientific
ISBN: 9814475467
Category : Mathematics
Languages : en
Pages : 789
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Book Description
This volume contains talks given at a joint meeting of three communities working in the fields of difference equations, special functions and applications (ISDE, OPSFA, and SIDE). The articles reflect the diversity of the topics in the meeting but have difference equations as common thread. Articles cover topics in difference equations, discrete dynamical systems, special functions, orthogonal polynomials, symmetries, and integrable difference equations.
Author: Saber Elaydi
Publisher: World Scientific
ISBN: 9812706437
Category : Science
Languages : en
Pages : 789
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Book Description
This volume contains talks given at a joint meeting of three communities working in the fields of difference equations, special functions and applications (ISDE, OPSFA, and SIDE). The articles reflect the diversity of the topics in the meeting but have difference equations as common thread. Articles cover topics in difference equations, discrete dynamical systems, special functions, orthogonal polynomials, symmetries, and integrable difference equations.
Author: Welington de Melo
Publisher: Springer Science & Business Media
ISBN: 3642780431
Category : Mathematics
Languages : en
Pages : 616
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Book Description
One-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the non-invertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory in one-dimensional dynamics. By reading one or more of the chapters, the reader can quickly reach the frontier of research. Let us quickly summarize the book. The first chapter deals with circle diffeomorphisms and contains a complete proof of the theorem on the smooth linearizability of circle diffeomorphisms due to M. Herman, J.-C. Yoccoz and others. Chapter II treats the kneading theory of Milnor and Thurstonj also included are an exposition on Hofbauer's tower construction and a result on fuB multimodal families (this last result solves a question posed by J. Milnor).
Author: Karen M. Brucks
Publisher: Cambridge University Press
ISBN: 9780521547666
Category : Mathematics
Languages : en
Pages : 316
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Book Description
One-dimensional dynamics owns many deep results and avenues of active mathematical research. Numerous inroads to this research exist for the advanced undergraduate or beginning graduate student. This book provides glimpses into one-dimensional dynamics with the hope that the results presented illuminate the beauty and excitement of the field. Much of this material is covered nowhere else in textbook format, some are mini new research topics in themselves, and novel connections are drawn with other research areas both inside and outside the text. The material presented here is not meant to be approached in a linear fashion. Readers are encouraged to pick and choose favourite topics. Anyone with an interest in dynamics, novice or expert alike, will find much of interest within.
