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Iterates Of Maps On An Interval

Author : C. Preston
ISBN : 9783540400554
Genre : Mathematics
File Size : 87. 65 MB
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Iterates Of Maps On An Interval

Author : Chris Preston
ISBN : OCLC:884521310
Genre :
File Size : 53. 2 MB
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Iterates Of Maps On An Interval

Author : Christopher J. Preston
ISBN : OCLC:157025796
Genre :
File Size : 85. 76 MB
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Iterates Of Piecewise Monotone Mappings On An Interval

Author : Chris Preston
ISBN : 9783540459712
Genre : Mathematics
File Size : 35. 23 MB
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Piecewise monotone mappings on an interval provide simple examples of discrete dynamical systems whose behaviour can be very complicated. These notes are concerned with the properties of the iterates of such mappings. The material presented can be understood by anyone who has had a basic course in (one-dimensional) real analysis. The account concentrates on the topological (as opposed to the measure theoretical) aspects of the theory of piecewise monotone mappings. As well as offering an elementary introduction to this theory, these notes also contain a more advanced treatment of the problem of classifying such mappings up to topological conjugacy.

Iterates Of Maps On An Interval

Author : Sivalingam Sivanesan
ISBN : OCLC:23350734
Genre : Functions of real variables
File Size : 85. 79 MB
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Chaotic Maps

Author : Goong Chen
ISBN : 9781598299144
Genre : Mathematics
File Size : 61. 16 MB
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This book consists of lecture notes for a semester-long introductory graduate course on dynamical systems and chaos taught by the authors at Texas A&M University and Zhongshan University, China. There are ten chapters in the main body of the book, covering an elementary theory of chaotic maps in finite-dimensional spaces. The topics include one-dimensional dynamical systems (interval maps), bifurcations, general topological, symbolic dynamical systems, fractals and a class of infinite-dimensional dynamical systems which are induced by interval maps, plus rapid fluctuations of chaotic maps as a new viewpoint developed by the authors in recent years. Two appendices are also provided in order to ease the transitions for the readership from discrete-time dynamical systems to continuous-time dynamical systems, governed by ordinary and partial differential equations. Table of Contents: Simple Interval Maps and Their Iterations / Total Variations of Iterates of Maps / Ordering among Periods: The Sharkovski Theorem / Bifurcation Theorems for Maps / Homoclinicity. Lyapunoff Exponents / Symbolic Dynamics, Conjugacy and Shift Invariant Sets / The Smale Horseshoe / Fractals / Rapid Fluctuations of Chaotic Maps on RN / Infinite-dimensional Systems Induced by Continuous-Time Difference Equations

Dynamics In One Dimension

Author : Louis S. Block
ISBN : 9783540470236
Genre : Mathematics
File Size : 88. 92 MB
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The behaviour under iteration of unimodal maps of an interval, such as the logistic map, has recently attracted considerable attention. It is not so widely known that a substantial theory has by now been built up for arbitrary continuous maps of an interval. The purpose of the book is to give a clear account of this subject, with complete proofs of many strong, general properties. In a number of cases these have previously been difficult of access. The analogous theory for maps of a circle is also surveyed. Although most of the results were unknown thirty years ago, the book will be intelligible to anyone who has mastered a first course in real analysis. Thus the book will be of use not only to students and researchers, but will also provide mathematicians generally with an understanding of how simple systems can exhibit chaotic behaviour.

Geometric Pressure For Multimodal Maps Of The Interval

Author : Feliks Przytycki
ISBN : 9781470435677
Genre : Conformal geometry
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This paper is an interval dynamics counterpart of three theories founded earlier by the authors, S. Smirnov and others in the setting of the iteration of rational maps on the Riemann sphere: the equivalence of several notions of non-uniform hyperbolicity, Geometric Pressure, and Nice Inducing Schemes methods leading to results in thermodynamical formalism. The authors work in a setting of generalized multimodal maps, that is, smooth maps f of a finite union of compact intervals Iˆ in R into R with non-flat critical points, such that on its maximal forward invariant set K the map f is topologically transitive and has positive topological entropy. They prove that several notions of non-uniform hyperbolicity of f|K are equivalent (including uniform hyperbolicity on periodic orbits, TCE & all periodic orbits in K hyperbolic repelling, Lyapunov hyperbolicity, and exponential shrinking of pull-backs). They prove that several definitions of geometric pressure P(t), that is pressure for the map f|K and the potential −tlog|f′|, give the same value (including pressure on periodic orbits, “tree” pressure, variational pressures and conformal pressure). Finally they prove that, provided all periodic orbits in K are hyperbolic repelling, the function P(t) is real analytic for t between the “condensation” and “freezing” parameters and that for each such t there exists unique equilibrium (and conformal) measure satisfying strong statistical properties.

Iterated Maps On The Interval As Dynamical Systems

Author : Pierre Collet
ISBN : UOM:39015028049503
Genre : Differentiable dynamical systems
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List of mathematical symbols

Iteration Of Piecewise Linear Maps On An Interval

Author : James B. McGuire
ISBN : 0868391719
Genre : Linear operators
File Size : 40. 88 MB
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Chaos On The Interval

Author : Sylvie Ruette
ISBN : 9781470429560
Genre : Chaotic behavior in systems
File Size : 87. 52 MB
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The aim of this book is to survey the relations between the various kinds of chaos and related notions for continuous interval maps from a topological point of view. The papers on this topic are numerous and widely scattered in the literature; some of them are little known, difficult to find, or originally published in Russian, Ukrainian, or Chinese. Dynamical systems given by the iteration of a continuous map on an interval have been broadly studied because they are simple but nevertheless exhibit complex behaviors. They also allow numerical simulations, which enabled the discovery of some chaotic phenomena. Moreover, the “most interesting” part of some higher-dimensional systems can be of lower dimension, which allows, in some cases, boiling it down to systems in dimension one. Some of the more recent developments such as distributional chaos, the relation between entropy and Li-Yorke chaos, sequence entropy, and maps with infinitely many branches are presented in book form for the first time. The author gives complete proofs and addresses both graduate students and researchers.

Combinatorial Patterns For Maps Of The Interval

Author : Michał Misiurewicz
ISBN : 9780821825136
Genre : Mathematics
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In recent years, motivated by Shrkovskii's theorem, researchers have realized that a good deal of information about the dynamics of a map on the interval can be deduced from the combinatorial structure of its periodic orbits. This data can be formulated as a forcing relation between cyclic permutations (representing orbit types of periodic orbits). The present study investigates a number of new features of this relation and its generalization to multicyclic permutations (modelling finite unions of periodic orbits) and combinatorial patterns (modelling finite invariant sets). A central theme is the role of reductions and extensions of permutations. Results include: (i) a combinatorial shadowing theorem and its application to approximating permutations by cycles in the forcing relation; (ii) the distribution of different representatives of a given cycle in one (adjusted) map; (iii) characterization of the forcing-maximal permutations and patterns of fixed degree; and (iv) a calculation of the asymptotic growth rate of the maximum entropy forced by a permutation of given degree.

Iteration Theory Proceedings Of The European Conference

Author : Forg-rob W
ISBN : 9789814547895
Genre :
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Effects of environmental, economic, social, political and technical factors have led to the rapid deployment of various sources of renewable energy-based power generation. The incorporation of these generation technologies have led to the development of a broad array of new methods and tools to integrate this new form of generation into the power system network. This book, arranged into six sections, highlights various renewable energy based generation technologies, and consists a series of papers written by experts in their respective fields of specialization.The Handbook of Renewable Energy Technology will be of great practical benefit to professionals, scientists and researchers in the relevant industries, and will be of interest to those of the general public wanting to know more about renewable energy technologies.

Spontaneous Formation Of Space Time Structures And Criticality

Author : T. Riste
ISBN : 9789401135085
Genre : Science
File Size : 44. 89 MB
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This volume contains the proceedings of a NATO Advanced study Institute held at Geilo, Norway between 2 - 12 april 1991. This institute was the eleventh in a series held biannually at Geilo on the subject of phase transitions. It was intended to capture the latest ideas on selforgan ized patterns and criticality. The Institute brought together many lecturers, students and active re searchers in the field from a wide range of NATO and non-NATO countries. The main financial support came from the NATO scientific Affairs Divi sion, but additional support was obtained from the Norwegian Research Council for Science and the Humanities (NAVF) and Institutt for energi teknikk. The organizers would like to thank all these contributors for their help in promoting an exciting and rewarding meeting, and in doing so are confident that they echo the appreciation of all the parti cipants. In cooperative, equilibrium systems, physical states are described by spatio-temporal correlation functions. The intimate connection between space and time correlations is especially apparent at the critical point, the second order phase transition, where the spatial range and the decay time of the correlation function both become infinite. The salient features of critical phenomena and the history of the devel opment of this field of science are treated in the first chapter of this book.

Symbolic Dynamics Of Trapezoidal Maps

Author : J.D. Louck
ISBN : 9789400946101
Genre : Mathematics
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It isn't that they can't see the solution. It is Approach your problems from the right end and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father The Hermit Gad in Crane Feathers' in R. Brown The point of a Pin'. van GuIik's The Chinese Maze Murders. Growing speciaIization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Thirty Years After Sharkovskii S Theorem New Perspectives Proceedings Of The Conference

Author : Luis Alseda
ISBN : 9789814548304
Genre :
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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.

Bifurcation Symmetry And Patterns

Author : Jorge Buescu
ISBN : 3764370203
Genre : Mathematics
File Size : 40. 16 MB
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The latest developments on both the theory and applications of bifurcations with symmetry. The text includes recent experimental work as well as new approaches to and applications of the theory to other sciences. It shows the range of dissemination of the work of Martin Golubitsky and Ian Stewart and its influence in modern mathematics at the same time as it contains work of young mathematicians in new directions. The range of topics includes mathematical biology, pattern formation, ergodic theory, normal forms, one-dimensional dynamics and symmetric dynamics.

The Nonlinear Workbook

Author : Willi-Hans Steeb
ISBN : 9789814583497
Genre : Science
File Size : 29. 41 MB
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The Nonlinear Workbook provides a comprehensive treatment of all the techniques in nonlinear dynamics together with C++, Java and SymbolicC++ implementations. The book not only covers the theoretical aspects of the topics but also provides the practical tools. To understand the material, more than 100 worked out examples and 160 ready to run programs are included. Each chapter provides a collection of interesting problems. New topics added to the 6th edition are Swarm Intelligence, Quantum Cellular Automata, Hidden Markov Model and DNA, Birkhoff's ergodic theorem and chaotic maps, Banach fixed point theorem and applications, tau-wavelets of Haar, Boolean derivatives and applications, and Cartan forms and Lagrangian. Request Inspection Copy

Nonlinear Workbook The Chaos Fractals Cellular Automata Neural Networks Genetic Algorithms Fuzzy Logic With C Java Symbolicc And Reduce Programs

Author : Willi-hans Steeb
ISBN : 9789814543491
Genre :
File Size : 45. 7 MB
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New Edition: The Nonlinear Workbook (6th Edition)This book provides all the techniques and methods used in nonlinear dynamics. All the concepts are discussed in detail. The numerical and symbolic methods are implemented using C++, Java, SymbolicC++ and Reduce.

Dynamics Reported

Author :
ISBN : 9783642612152
Genre : Mathematics
File Size : 87. 40 MB
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DYNAMICS REPORTED reports on recent developments in dynamical systems. Dynamical systems of course originated from ordinary differential equations. Today, dynamical systems cover a much larger area, including dynamical processes described by functional and integral equations, by partial and stochastic differential equations, etc. Dynamical systems have involved remarkably in recent years. A wealth of new phenomena, new ideas and new techniques are proving to be of considerable interest to scientists in rather different fields. It is not surprising that thousands of publications on the theory itself and on its various applications are appearing DYNAMICS REPORTED presents carefully written articles on major subjects in dy namical systems and their applications, addressed not only to specialists but also to a broader range of readers including graduate students. Topics are advanced, while detailed exposition of ideas, restriction to typical results - rather than the most general one- and, last but not least, lucid proofs help to gain the utmost degree of clarity. It is hoped, that DYNAMICS REPORTED will be useful for those entering the field and will stimulate an exchange of ideas among those working in dynamical systems Summer 1991 Christopher K. R. T Jones Drs Kirchgraber Hans-Otto Walther Managing Editors Table of Contents The "Spectral" Decomposition for One-Dimensional Maps Alexander M. Blokh Introduction and Main Results 1. 1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 0. 1. 1. Historical Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 2. A Short Description of the Approach Presented . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 3. Solenoidal Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Basic Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. 4.

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