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Chaotic Maps Fractals And Rapid Fluctuations

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Chaotic Maps

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Author : Goong Chen
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2011-09-09

Chaotic Maps written by Goong Chen and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-09 with Technology & Engineering categories.

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

Chaotic Maps Fractals And Rapid Fluctuations

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Author : Liangliang Li
language : en
Publisher: Springer Nature
Release Date : 2025-07-15

Chaotic Maps Fractals And Rapid Fluctuations written by Liangliang Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-15 with Mathematics categories.

This book was developed from lecture notes for an introductory graduate course and provides an essential introduction to chaotic maps in finite-dimensional spaces. Furthermore, the authors show how to apply this theory to infinite-dimensional systems corresponding to partial differential equations to study chaotic vibration of the wave equation subject to various types of nonlinear boundary conditions. The book provides background on chaos as a highly interesting nonlinear phenomenon and explains why it is one of the most important scientific findings of the past three decades. In addition, the book covers key topics including one-dimensional dynamical systems, bifurcations, general topological, symbolic dynamical systems, and fractals. The authors also show a class of infinite-dimensional nonlinear dynamical systems, which are reducible to interval maps, plus rapid fluctuations of chaotic maps. This second edition includes updated and expanded chapters as well as additional problems.

Chaotic Maps

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Author : Liangliang Li
language : en
Publisher:
Release Date : 2025-05-28

Chaotic Maps written by Liangliang Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-28 with Language Arts & Disciplines categories.

Chaotic Maps

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Author : Goong Chen
language : en
Publisher: Springer Nature
Release Date : 2022-05-31

Chaotic Maps written by Goong Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Mathematics categories.

Dynamics With Chaos And Fractals

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Author : Marat Akhmet
language : en
Publisher: Springer Nature
Release Date : 2020-01-01

Dynamics With Chaos And Fractals written by Marat Akhmet and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-01 with Mathematics categories.

The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested.

Advances In Asset Management And Condition Monitoring

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Author : Andrew Ball
language : en
Publisher: Springer Nature
Release Date : 2020-08-27

Advances In Asset Management And Condition Monitoring written by Andrew Ball and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-27 with Technology & Engineering categories.

This book gathers select contributions from the 32nd International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management (COMADEM 2019), held at the University of Huddersfield, UK in September 2019, and jointly organized by the University of Huddersfield and COMADEM International. The aim of the Congress was to promote awareness of the rapidly emerging interdisciplinary areas of condition monitoring and diagnostic engineering management. The contents discuss the latest tools and techniques in the multidisciplinary field of performance monitoring, root cause failure modes analysis, failure diagnosis, prognosis, and proactive management of industrial systems. There is a special focus on digitally enabled asset management and covers several topics such as condition monitoring, maintenance, structural health monitoring, non-destructive testing and other allied areas. Bringing together expert contributions from academia and industry, this book will be a valuable resource for those interested in latest condition monitoring and asset management techniques.

Metaheuristics

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Author : Luca Di Gaspero
language : en
Publisher: Springer Nature
Release Date : 2023-02-22

Metaheuristics written by Luca Di Gaspero and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-22 with Computers categories.

This book constitutes the refereed proceedings of the 14th International Conference on Metaheuristics, MIC 2022, held in Syracuse, Italy, in July 2022. The 48 full papers together with 17 short papers presented were carefully reviewed and selected from 72 submissions. The papers detail metaheuristic techniques. Chapter “Evaluating the Effects of Chaos in Variable Neighbourhood Search” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Fast Start Integral Calculus

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Author : Daniel Ashlock
language : en
Publisher: Springer Nature
Release Date : 2022-05-31

Fast Start Integral Calculus written by Daniel Ashlock and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Mathematics categories.

This book introduces integrals, the fundamental theorem of calculus, initial value problems, and Riemann sums. It introduces properties of polynomials, including roots and multiplicity, and uses them as a framework for introducing additional calculus concepts including Newton's method, L'Hôpital's Rule, and Rolle's theorem. Both the differential and integral calculus of parametric, polar, and vector functions are introduced. The book concludes with a survey of methods of integration, including u-substitution, integration by parts, special trigonometric integrals, trigonometric substitution, and partial fractions.

Fast Start Differential Calculus

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Author : Daniel Ashlock
language : en
Publisher: Springer Nature
Release Date : 2022-06-01

Fast Start Differential Calculus written by Daniel Ashlock and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Mathematics categories.

This book reviews the algebraic prerequisites of calculus, including solving equations, lines, quadratics, functions, logarithms, and trig functions. It introduces the derivative using the limit-based definition and covers the standard function library and the product, quotient, and chain rules. It explores the applications of the derivative to curve sketching and optimization and concludes with the formal definition of the limit, the squeeze theorem, and the mean value theorem.

Fast Start Advanced Calculus

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Author : Daniel Ashlock
language : en
Publisher: Springer Nature
Release Date : 2022-06-01

Fast Start Advanced Calculus written by Daniel Ashlock and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Mathematics categories.

This book continues the material in two early Fast Start calculus volumes to include multivariate calculus, sequences and series, and a variety of additional applications. These include partial derivatives and the optimization techniques that arise from them, including Lagrange multipliers. Volumes of rotation, arc length, and surface area are included in the additional applications of integration. Using multiple integrals, including computing volume and center of mass, is covered. The book concludes with an initial treatment of sequences, series, power series, and Taylor's series, including techniques of function approximation.

Chaotic Maps Fractals And Rapid Fluctuations

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