Iterated Maps On The Interval As Dynamical Systems
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Iterated Maps On The Interval As Dynamical Systems
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Author : Pierre Collet
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-25
Iterated Maps On The Interval As Dynamical Systems written by Pierre Collet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-25 with Social Science categories.
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 .
Iterated Maps On The Interval As Dynamical Systems
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Author : Pierre Collet
language : en
Publisher:
Release Date : 1986
Iterated Maps On The Interval As Dynamical Systems written by Pierre Collet and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Concepts And Results In Chaotic Dynamics A Short Course
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Author : Pierre Collet
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-07
Concepts And Results In Chaotic Dynamics A Short Course written by Pierre Collet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-07 with Mathematics categories.
The study of dynamical systems is a well established field. This book provides a panorama of several aspects of interest to mathematicians and physicists. It collects the material of several courses at the graduate level given by the authors, avoiding detailed proofs in exchange for numerous illustrations and examples. Apart from common subjects in this field, a lot of attention is given to questions of physical measurement and stochastic properties of chaotic dynamical systems.
Bifurcations
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Author : Takashi Matsumoto
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Bifurcations written by Takashi Matsumoto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Bifurcation originally meant "splitting into two parts. " Namely, a system under goes a bifurcation when there is a qualitative change in the behavior of the sys tem. Bifurcation in the context of dynamical systems, where the time evolution of systems are involved, has been the subject of research for many scientists and engineers for the past hundred years simply because bifurcations are interesting. A very good way of understanding bifurcations would be to see them first and study theories second. Another way would be to first comprehend the basic concepts and theories and then see what they look like. In any event, it is best to both observe experiments and understand the theories of bifurcations. This book attempts to provide a general audience with both avenues toward understanding bifurcations. Specifically, (1) A variety of concrete experimental results obtained from electronic circuits are given in Chapter 1. All the circuits are very simple, which is crucial in any experiment. The circuits, however, should not be too simple, otherwise nothing interesting can happen. Albert Einstein once said "as simple as pos sible, but no more" . One of the major reasons for the circuits discussed being simple is due to their piecewise-linear characteristics. Namely, the voltage current relationships are composed of several line segments which are easy to build. Piecewise-linearity also simplifies rigorous analysis in a drastic man ner. (2) The piecewise-linearity of the circuits has far reaching consequences.
One Dimensional Dynamics
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Author : Welington de Melo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
One Dimensional Dynamics written by Welington de Melo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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).
Mathematical Constants
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Author : Steven R. Finch
language : en
Publisher: Cambridge University Press
Release Date : 2003-08-18
Mathematical Constants written by Steven R. Finch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-18 with Mathematics categories.
Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Collected Papers Of John Milnor
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Author : John Willard Milnor
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Collected Papers Of John Milnor written by John Willard Milnor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Algebra categories.
Iteration Theory Proceedings Of The European Conference
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Author : C Simo
language : en
Publisher: #N/A
Release Date : 1991-07-22
Iteration Theory Proceedings Of The European Conference written by C Simo and has been published by #N/A this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-07-22 with categories.
The main topics of this proceedings stress the interactions between the theory of functional equations and the theory of dynamical systems. A total of 38 invited lectures are included.
Proceedings Of The Eighth International Conference On Difference Equations And Applications
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Author : Saber N. Elaydi
language : en
Publisher: CRC Press
Release Date : 2005-04-29
Proceedings Of The Eighth International Conference On Difference Equations And Applications written by Saber N. Elaydi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-29 with Mathematics categories.
The Eighth International Conference on Difference Equations and Applications was held at Masaryk University in Brno, Czech Republic. This volume comprises refereed papers presented at this conference. These papers cover all important themes, conjectures, and open problems in the fields of discrete dynamical systems and ordinary and partial differen
Fractal Geometry And Applications A Jubilee Of Benoit Mandelbrot
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Author : Michel Laurent Lapidus
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Fractal Geometry And Applications A Jubilee Of Benoit Mandelbrot written by Michel Laurent Lapidus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.