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| Author | : E. Roy Pike |
| Publisher | : CRC Press |
| Total Pages | : 282 |
| Release | : 2020-08-27 |
| Genre | : Mathematics |
| ISBN | : 1000156915 |
Download Chaos, Noise and Fractals Book in PDF, ePub and Kindle
The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.
| Author | : Andrzej Lasota |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 481 |
| Release | : 2013-11-27 |
| Genre | : Mathematics |
| ISBN | : 146124286X |
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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.
| Author | : Andrzej Lasota |
| Publisher | : |
| Total Pages | : 492 |
| Release | : 2014-09-01 |
| Genre | : |
| ISBN | : 9781461242871 |
Download Chaos, Fractals, and Noise Book in PDF, ePub and Kindle
| Author | : Paul S. Addison |
| Publisher | : CRC Press |
| Total Pages | : 276 |
| Release | : 1997-01-01 |
| Genre | : Science |
| ISBN | : 9780849384431 |
Download Fractals and Chaos Book in PDF, ePub and Kindle
Fractals and Chaos: An Illustrated Course provides you with a practical, elementary introduction to fractal geometry and chaotic dynamics-subjects that have attracted immense interest throughout the scientific and engineering disciplines. The book may be used in part or as a whole to form an introductory course in either or both subject areas. A prominent feature of the book is the use of many illustrations to convey the concepts required for comprehension of the subject. In addition, plenty of problems are provided to test understanding. Advanced mathematics is avoided in order to provide a concise treatment and speed the reader through the subject areas. The book can be used as a text for undergraduate courses or for self-study.
| Author | : A.J. Crilly |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 278 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461230349 |
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This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot in the late 1970s, but objects now defined as fractal in form have been known to artists and mathematicians for centuries. Mandelbrot's definition-"a set whose Hausdorff dimension is not an integer" -is clear in mathematical terms. In addition, related concepts are those of self-similarity and sub-divisibility. A fractal object is self-similar in that subsections of the object are similar in some sense to the whole object.
| Author | : A.J. Crilly |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 312 |
| Release | : 2013-11-11 |
| Genre | : Computers |
| ISBN | : 3642780970 |
Download Applications of Fractals and Chaos Book in PDF, ePub and Kindle
Applications of Fractals and Chaos presents new developments in this rapidlydeveloping subject area. The presentation is more than merely theoretical, it specifically presents particular applications in a wide range of applications areas. Under the oceans, we consider the ways in which sponges and corals grow; we look, too, at the stability of ships on their surfaces. Land itself is modelled and applications to art, medicineand camouflage are presented. Readers should find general interest in the range of areas considered and should also be able to discover methods of value for their own specific areas of interest from studying the structure of related activities.
| Author | : Fischer |
| Publisher | : CRC Press |
| Total Pages | : 282 |
| Release | : 1985-06-03 |
| Genre | : Science |
| ISBN | : 9780824773250 |
Download Chaos, Fractals, and Dynamics Book in PDF, ePub and Kindle
This timely work focuses on the recent expansion of research in the field of dynamical systems theory with related studies of chaos and fractals. Integrating the work of leading mathematicians, physicists, chemists, and engineers, this research-level monograph discusses different aspects of the concepts of chaos and fractals from both experimental and theoretical points of view. Featuring the most recent advances-including findings made possible by the development of digital computers-this authoritative work provides thorough understanding of known behavior of nonlinear dynamical systems as well as considerable insight into complex aspects not yet well understood. With a broad, multidisciplinary perspective and an ample supply of literature citations, Chaos, Fractals, and Dynamics is an invaluable reference and starting point for further research for scientists in all fields utilizing dynamical systems theory, including applied mathematicians, physicists, dynamists, chemists, biomathematicians, and graduate students in these areas. Book jacket.
| Author | : Gary Drzewiecki |
| Publisher | : Springer Nature |
| Total Pages | : 142 |
| Release | : 2022-01-01 |
| Genre | : Technology & Engineering |
| ISBN | : 3030889688 |
Download Fundamentals of Chaos and Fractals for Cardiology Book in PDF, ePub and Kindle
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.
| Author | : Heinz-Otto Peitgen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1013 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475747403 |
Download Chaos and Fractals Book in PDF, ePub and Kindle
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.
| Author | : Donald L. Turcotte |
| Publisher | : Cambridge University Press |
| Total Pages | : 424 |
| Release | : 1997-07-13 |
| Genre | : Mathematics |
| ISBN | : 9780521567336 |
Download Fractals and Chaos in Geology and Geophysics Book in PDF, ePub and Kindle
The fundamental concepts of fractal geometry and chaotic dynamics, along with the related concepts of multifractals, self-similar time series, wavelets, and self-organized criticality, are introduced in this book, for a broad range of readers interested in complex natural phenomena. Now in a greatly expanded, second edition, this book relates fractals and chaos to a variety of geological and geophysical applications. All concepts are introduced at the lowest possible level of mathematics consistent with their understanding, so that the reader requires only a background in basic physics and mathematics.
