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Chaos Fractals And Dynamics
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Book Synopsis Chaos, Fractals, and Dynamics by : Robert L. Devaney
Download or read book Chaos, Fractals, and Dynamics written by Robert L. Devaney and published by Addison Wesley Publishing Company. This book was released on 1990 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the mathematical topics of chaos, fractals, and dynamics using a combination of hands-on computer experimentation and precalculas mathmetics. A series of experiments produce fascinating computer graphics images of Julia sets, the Mandelbrot set, and fractals. The basic ideas of dynamics--chaos, iteration, and stability--are illustrated via computer projects.
Book Synopsis Chaos, Fractals, and Noise by : Andrzej Lasota
Download or read book Chaos, Fractals, and Noise written by Andrzej Lasota and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book was originally published in 1985 under the ti tle "Probabilistic Properties of Deterministic Systems. " In the intervening years, interest in so-called "chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter.
Book Synopsis Dynamics with Chaos and Fractals by : Marat Akhmet
Download or read book Dynamics with Chaos and Fractals written by Marat Akhmet and published by Springer Nature. This book was released on 2020-01-01 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Chaos and Fractals by : Heinz-Otto Peitgen
Download or read book Chaos and Fractals written by Heinz-Otto Peitgen and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 1013 pages. Available in PDF, EPUB and Kindle. Book excerpt: For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.
Book Synopsis Chaotic and Fractal Dynamics by : Francis C. Moon
Download or read book Chaotic and Fractal Dynamics written by Francis C. Moon and published by John Wiley & Sons. This book was released on 2008-11-20 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: A revision of a professional text on the phenomena of chaotic vibrations in fluids and solids. Major changes reflect the latest developments in this fast-moving topic, the introduction of problems to every chapter, additional mathematics and applications, more coverage of fractals, numerous computer and physical experiments. Contains eight pages of 4-color pictures.
Book Synopsis Chaotic Dynamics and Fractals by : Michael F. Barnsley
Download or read book Chaotic Dynamics and Fractals written by Michael F. Barnsley and published by Academic Press. This book was released on 2014-05-10 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaotic Dynamics and Fractals covers the proceedings of the 1985 Conference on Chaotic Dynamics, held at the Georgia Institute of Technology. This conference deals with the research area of chaos, dynamical systems, and fractal geometry. This text is organized into three parts encompassing 16 chapters. The first part describes the nature of chaos and fractals, the geometric tool for some strange attractors, and other complicated sets of data associated with chaotic systems. This part also considers the Henon-Hiles Hamiltonian with complex time, a Henon family of maps from C2 into itself, and the idea of turbulent maps in the course of presenting results on iteration of continuous maps from the unit interval to itself. The second part discusses complex analytic dynamics and associated fractal geometry, specifically the bursts into chaos, algorithms for obtaining geometrical and combinatorial information, and the parameter space for iterated cubic polynomials. This part also examines the differentiation of Julia sets with respects to a parameter in the associated rational map, permitting the formulation of Taylor series expansion for the sets. The third part highlights the applications of chaotic dynamics and fractals. This book will prove useful to mathematicians, physicists, and other scientists working in, or introducing themselves to, the field.
Book Synopsis Chaotic Vibrations by : Francis C. Moon
Download or read book Chaotic Vibrations written by Francis C. Moon and published by Wiley-VCH. This book was released on 2004-06-07 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translates new mathematical ideas in nonlinear dynamics and chaos into a language that engineers and scientists can understand, and gives specific examples and applications of chaotic dynamics in the physical world. Also describes how to perform both computer and physical experiments in chaotic dynamics. Topics cover Poincare maps, fractal dimensions and Lyapunov exponents, illustrating their use in specific physical examples. Includes an extensive guide to the literature, especially that relating to more mathematically oriented works; a glossary of chaotic dynamics terms; a list of computer experiments; and details for a demonstration experiment on chaotic vibrations.
Book Synopsis Fractals, Chaos, Power Laws by : Manfred Schroeder
Download or read book Fractals, Chaos, Power Laws written by Manfred Schroeder and published by Courier Corporation. This book was released on 2009-08-21 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author -- hailed by Publishers Weekly as a modern Lewis Carroll -- conveys memorable insights in the form of puns and puzzles. 1992 edition.
Book Synopsis Chaos and Fractals by : David P. Feldman
Download or read book Chaos and Fractals written by David P. Feldman and published by Oxford University Press, USA. This book was released on 2012-08-09 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: For students with a background in elementary algebra, this book provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia Sets and the Mandelbrot Set, power laws, and cellular automata. The book includes over 200 end-of-chapter exercises.
Book Synopsis Chaotic Dynamics by : Geoffrey R. Goodson
Download or read book Chaotic Dynamics written by Geoffrey R. Goodson and published by Cambridge University Press. This book was released on 2017 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This rigorous undergraduate introduction to dynamical systems is an accessible guide for mathematics students advancing from calculus.
Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz
Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Book Synopsis Fundamentals of Chaos and Fractals for Cardiology by : Gary Drzewiecki
Download or read book Fundamentals of Chaos and Fractals for Cardiology written by Gary Drzewiecki and published by Springer Nature. This book was released on 2022-01-01 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook serves as an introduction to nonlinear dynamics and fractals for physiological modeling. Examples and demonstrations from current research in cardiopulmonary engineering and neuro-systems engineering are provided, as well as lab and computer exercises that encourage readers to apply the course material. This is an ideal textbook for graduate students in biomedical engineering departments, researchers who analyze physiological data, and researchers interested in physiological modeling.
Book Synopsis Chaotic Dynamics by : Gregory L. Baker
Download or read book Chaotic Dynamics written by Gregory L. Baker and published by Cambridge University Press. This book was released on 1996 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level. It was widely praised for the clarity of writing and for the unique and effective way in which the authors presented the basic ideas. These same qualities characterize this revised and expanded second edition. Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had a far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second- and third-year level.
Book Synopsis An Introduction To Chaotic Dynamical Systems by : Robert Devaney
Download or read book An Introduction To Chaotic Dynamical Systems written by Robert Devaney and published by CRC Press. This book was released on 2018-03-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.
Download or read book Chaos written by Kathleen Alligood and published by Springer. This book was released on 2012-12-06 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.
Book Synopsis Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics by : Rainer Klages
Download or read book Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics written by Rainer Klages and published by World Scientific. This book was released on 2007 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: A valuable introduction for newcomers as well as an important reference and source of inspiration for established researchers, this book provides an up-to-date summary of central topics in the field of nonequilibrium statistical mechanics and dynamical systems theory.Understanding macroscopic properties of matter starting from microscopic chaos in the equations of motion of single atoms or molecules is a key problem in nonequilibrium statistical mechanics. Of particular interest both for theory and applications are transport processes such as diffusion, reaction, conduction and viscosity.Recent advances towards a deterministic theory of nonequilibrium statistical physics are summarized: Both Hamiltonian dynamical systems under nonequilibrium boundary conditions and non-Hamiltonian modelings of nonequilibrium steady states by using thermal reservoirs are considered. The surprising new results include transport coefficients that are fractal functions of control parameters, fundamental relations between transport coefficients and chaos quantities, and an understanding of nonequilibrium entropy production in terms of fractal measures and attractors.The theory is particularly useful for the description of many-particle systems with properties in-between conventional thermodynamics and nonlinear science, as they are frequently encountered on nanoscales.
Book Synopsis A Student's Guide to Maxwell's Equations by : Daniel Fleisch
Download or read book A Student's Guide to Maxwell's Equations written by Daniel Fleisch and published by Cambridge University Press. This book was released on 2008-01-10 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere–Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.
