Fractal Dimensions For Poincare Recurrences

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Fractal Dimensions for Poincare Recurrences

Author : Valentin Afraimovich
Publisher : Elsevier
ISBN 13 : 0080462391
Total Pages : 258 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Fractal Dimensions for Poincare Recurrences by : Valentin Afraimovich

Download or read book Fractal Dimensions for Poincare Recurrences written by Valentin Afraimovich and published by Elsevier. This book was released on 2006-06-21 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to an important branch of the dynamical systems theory : the study of the fine (fractal) structure of Poincare recurrences -instants of time when the system almost repeats its initial state. The authors were able to write an entirely self-contained text including many insights and examples, as well as providing complete details of proofs. The only prerequisites are a basic knowledge of analysis and topology. Thus this book can serve as a graduate text or self-study guide for courses in applied mathematics or nonlinear dynamics (in the natural sciences). Moreover, the book can be used by specialists in applied nonlinear dynamics following the way in the book. The authors applied the mathematical theory developed in the book to two important problems: distribution of Poincare recurrences for nonpurely chaotic Hamiltonian systems and indication of synchronization regimes in coupled chaotic individual systems.* Portions of the book were published in an article that won the title "month's new hot paper in the field of Mathematics" in May 2004* Rigorous mathematical theory is combined with important physical applications* Presents rules for immediate action to study mathematical models of real systems* Contains standard theorems of dynamical systems theory

Mathematical Techniques of Fractional Order Systems

Author : Ahmad Taher Azar
Publisher : Elsevier
ISBN 13 : 012813593X
Total Pages : 702 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Mathematical Techniques of Fractional Order Systems by : Ahmad Taher Azar

Download or read book Mathematical Techniques of Fractional Order Systems written by Ahmad Taher Azar and published by Elsevier. This book was released on 2018-06-11 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from different perspectives in design, analysis and realizations, nonlinear fractional-order circuits and systems, the fractional-order memristive circuits and systems in design, analysis, emulators, simulation and experimental results. It is primarily meant for researchers from academia and industry, and for those working in areas such as control engineering, electrical engineering, computer science and information technology. This book is ideal for researchers working in the area of both continuous-time and discrete-time dynamics and chaotic systems. - Discusses multidisciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results - Includes circuits and systems based on new nonlinear elements - Covers most of the linear and nonlinear fractional-order theorems that will solve many scientific issues for researchers - Closes the gap between theoretical approaches and real-world applications - Provides MATLAB® and Simulink code for many applications in the book

Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot

Author : Michel Laurent Lapidus
Publisher : American Mathematical Soc.
ISBN 13 : 9780821836378
Total Pages : 760 pages
Book Rating : 4.8/5 (363 download)

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Book Synopsis Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot by : Michel Laurent Lapidus

Download or read book Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot written by Michel Laurent Lapidus and published by American Mathematical Soc.. This book was released on 2004 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Chaos, Kinetics and Nonlinear Dynamics in Fluids and Plasmas

Author : Sadruddin Benkadda
Publisher : Springer Science & Business Media
ISBN 13 : 9783540646358
Total Pages : 462 pages
Book Rating : 4.6/5 (463 download)

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Book Synopsis Chaos, Kinetics and Nonlinear Dynamics in Fluids and Plasmas by : Sadruddin Benkadda

Download or read book Chaos, Kinetics and Nonlinear Dynamics in Fluids and Plasmas written by Sadruddin Benkadda and published by Springer Science & Business Media. This book was released on 1998-07-16 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last few years it has become apparent that fluid turbulence shares many common features with plasma turbulence, such as coherent structures and self-organization phenomena, passive scalar transport and anomalous diffusion. This book gathers very high level, current papers on these subjects. It is intended for scientists and researchers, lecturers and graduate students because of the review style of the papers.

Physics Of Chaos In Hamiltonian Systems, The (2nd Edition)

Author : George Zaslavsky
Publisher : World Scientific
ISBN 13 : 1908979232
Total Pages : 337 pages
Book Rating : 4.9/5 (89 download)

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Book Synopsis Physics Of Chaos In Hamiltonian Systems, The (2nd Edition) by : George Zaslavsky

Download or read book Physics Of Chaos In Hamiltonian Systems, The (2nd Edition) written by George Zaslavsky and published by World Scientific. This book was released on 2007-05-21 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to familiarize the reader with the essential properties of the chaotic dynamics of Hamiltonian systems by avoiding specialized mathematical tools, thus making it easily accessible to a broader audience of researchers and students. Unique material on the most intriguing and fascinating topics of unsolved and current problems in contemporary chaos theory is presented. The coverage includes: separatrix chaos; properties and a description of systems with non-ergodic dynamics; the distribution of Poincaré recurrences and their role in transport theory; dynamical models of the Maxwell's Demon, the occurrence of persistent fluctuations, and a detailed discussion of their role in the problem underlying the foundation of statistical physics; the emergence of stochastic webs in phase space and their link to space tiling with periodic (crystal type) and aperiodic (quasi-crystal type) symmetries.This second edition expands on pseudochaotic dynamics with weak mixing and the new phenomenon of fractional kinetics, which is crucial to the transport properties of chaotic motion.The book is ideally suited to all those who are actively working on the problems of dynamical chaos as well as to those looking for new inspiration in this area. It introduces the physicist to the world of Hamiltonian chaos and the mathematician to actual physical problems.The material can also be used by graduate students./a

The Physics of Chaos in Hamiltonian Systems

Author : George M. Zaslavsky
Publisher : World Scientific
ISBN 13 : 1860947956
Total Pages : 337 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis The Physics of Chaos in Hamiltonian Systems by : George M. Zaslavsky

Download or read book The Physics of Chaos in Hamiltonian Systems written by George M. Zaslavsky and published by World Scientific. This book was released on 2007 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to familiarize the reader with the essential properties of the chaotic dynamics of Hamiltonian systems by avoiding specialized mathematical tools, thus making it easily accessible to a broader audience of researchers and students. Unique material on the most intriguing and fascinating topics of unsolved and current problems in contemporary chaos theory is presented. The coverage includes: separatrix chaos; properties and a description of systems with non-ergodic dynamics; the distribution of Poincar recurrences and their role in transport theory; dynamical models of the Maxwell's Demon, the occurrence of persistent fluctuations, and a detailed discussion of their role in the problem underlying the foundation of statistical physics; the emergence of stochastic webs in phase space and their link to space tiling with periodic (crystal type) and aperiodic (quasi-crystal type) symmetries. This second edition expands on pseudochaotic dynamics with weak mixing and the new phenomenon of fractional kinetics, which is crucial to the transport properties of chaotic motion. The book is ideally suited to all those who are actively working on the problems of dynamical chaos as well as to those looking for new inspiration in this area. It introduces the physicist to the world of Hamiltonian chaos and the mathematician to actual physical problems.The material can also be used by graduate students.

Ergodic Theory

Author : Cesar E. Silva
Publisher : Springer Nature
ISBN 13 : 1071623885
Total Pages : 707 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Ergodic Theory by : Cesar E. Silva

Download or read book Ergodic Theory written by Cesar E. Silva and published by Springer Nature. This book was released on 2023-07-31 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras

Fractal Functions, Fractal Surfaces, and Wavelets

Author : Peter R. Massopust
Publisher : Academic Press
ISBN 13 : 0128044705
Total Pages : 428 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Fractal Functions, Fractal Surfaces, and Wavelets by : Peter R. Massopust

Download or read book Fractal Functions, Fractal Surfaces, and Wavelets written by Peter R. Massopust and published by Academic Press. This book was released on 2016-09-02 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets. The book is based on Massopust's work on and contributions to the theory of fractal interpolation, and the author uses a number of tools—including analysis, topology, algebra, and probability theory—to introduce readers to this exciting subject. Though much of the material presented in this book is relatively current (developed in the past decades by the author and his colleagues) and fairly specialized, an informative background is provided for those entering the field. With its coherent and comprehensive presentation of the theory of univariate and multivariate fractal interpolation, this book will appeal to mathematicians as well as to applied scientists in the fields of physics, engineering, biomathematics, and computer science. In this second edition, Massopust includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, further develops the connections to wavelets and wavelet sets, and deepens and extends the pedagogical content. - Offers a comprehensive presentation of fractal functions and fractal surfaces - Includes latest developments in fractal interpolation - Connects fractal geometry with wavelet theory - Includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, and further develops the connections to wavelets and wavelet sets - Deepens and extends the pedagogical content

Recent Developments in Fractals and Related Fields

Author : Julien Barral
Publisher : Birkhäuser
ISBN 13 : 3319578057
Total Pages : 320 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Recent Developments in Fractals and Related Fields by : Julien Barral

Download or read book Recent Developments in Fractals and Related Fields written by Julien Barral and published by Birkhäuser. This book was released on 2017-08-23 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.

Abstracts of Papers Presented to the American Mathematical Society

Author : American Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 666 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Abstracts of Papers Presented to the American Mathematical Society by : American Mathematical Society

Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 2002 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Chaos, Dynamics, and Fractals

Author : Joseph L. McCauley
Publisher : Cambridge University Press
ISBN 13 : 1107393272
Total Pages : 352 pages
Book Rating : 4.1/5 (73 download)

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Book Synopsis Chaos, Dynamics, and Fractals by : Joseph L. McCauley

Download or read book Chaos, Dynamics, and Fractals written by Joseph L. McCauley and published by Cambridge University Press. This book was released on 1994-05-26 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided in computation or experiment. This leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized in computation or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed.

Nonlinear Brain Dynamics

Author : Cornelis J. Stam
Publisher : Nova Publishers
ISBN 13 : 9781594548796
Total Pages : 166 pages
Book Rating : 4.5/5 (487 download)

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Book Synopsis Nonlinear Brain Dynamics by : Cornelis J. Stam

Download or read book Nonlinear Brain Dynamics written by Cornelis J. Stam and published by Nova Publishers. This book was released on 2006 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the beginning of the 21st century, understanding the brain has become one of the final frontiers of science. Hailed as the 'most complex object in the universe' the brain still defies a complete understanding of its workings, in particular in relation to consciousness and higher brain functions. Despite enormous scientific efforts, the question how the 'mere matter' of 1011 interacting nerve cells can give rise to the inner world of our subjective feelings still remains an enigma. However, in contrast to a few decades ago, when respectable neuroscience was not expected to deal with such questions, the search for brain/mind relationships has now become the focus of intense research. The central idea of this book: to understand the brain, we need to understand its dynamics.

Fractals in Probability and Analysis

Author : Christopher J. Bishop
Publisher : Cambridge University Press
ISBN 13 : 1107134110
Total Pages : 415 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Fractals in Probability and Analysis by : Christopher J. Bishop

Download or read book Fractals in Probability and Analysis written by Christopher J. Bishop and published by Cambridge University Press. This book was released on 2017 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.

Discrete and Continuous Dynamical Systems

Author :
Publisher :
ISBN 13 :
Total Pages : 432 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Discrete and Continuous Dynamical Systems by :

Download or read book Discrete and Continuous Dynamical Systems written by and published by . This book was released on 2004 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 916 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Regularity and Stochasticity of Nonlinear Dynamical Systems

Author : Dimitri Volchenkov
Publisher : Springer
ISBN 13 : 3319580620
Total Pages : 316 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Regularity and Stochasticity of Nonlinear Dynamical Systems by : Dimitri Volchenkov

Download or read book Regularity and Stochasticity of Nonlinear Dynamical Systems written by Dimitri Volchenkov and published by Springer. This book was released on 2017-06-24 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing on impulsive differential equations, from chaos to order in coupled oscillators, and differential-invariant solutions for automorphic systems, inequality under uncertainty.

Nonlinear Dynamics

Author : George Datseris
Publisher : Springer Nature
ISBN 13 : 3030910326
Total Pages : 243 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Nonlinear Dynamics by : George Datseris

Download or read book Nonlinear Dynamics written by George Datseris and published by Springer Nature. This book was released on 2022-03-13 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at students and researchers in all the diverse fields in which nonlinear phenomena are important. Since most tasks in nonlinear dynamics cannot be treated analytically, skills in using numerical simulations are crucial for analyzing these phenomena. The text therefore addresses in detail appropriate computational methods as well as identifying the pitfalls of numerical simulations. It includes numerous executable code snippets referring to open source Julia software packages. Each chapter includes a selection of exercises with which students can test and deepen their skills.