Chaos, Dynamics, and Fractals Paperback: An Algorithmic Approach to Deterministic Chaos: 2 (Cambridge Nonlinear Science Series, Series Number 2) - Softcover

McCauley, Joseph

Softcover

ISBN 10: 0521467470 ISBN 13: 9780521467476

Verlag: Cambridge University Press, 2010

Inhaltsangabe

The author presents deterministic chaos from the standpoint of theoretical computer arithmetic, leading to universal properties described by symbolic dynamics.

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Über die Autorin bzw. den Autor

Charlotte y Peter Fiell son dos autoridades en historia, teoría y crítica del diseño y han escrito más de sesenta libros sobre la materia, muchos de los cuales se han convertido en éxitos de ventas. También han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Diseño del siglo XX, El diseño industrial de la A a la Z, Scandinavian Design y Diseño del siglo XXI.

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This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the method of analysis and choice of emphasis make it very different from all other books in the field. It is written to provide 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 book is written especially for those who want clear answers to the following sorts of question: How can a deterministic trajectory be unpredictable? How can one compute nonperiodic chaotic trajectories with controlled precision? Can a deterministic trajectory be random? What are multifractals and where do they come from? What is turbulence and what has it to do with chaos and multifractals? And, finally, why is it not merely convenient, but also necessary, to study classes of iterated maps instead of differential equations when one wants predictions that are applicable to computation and experiment? Throughout the book the author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision is a fact of life that cannot be avoided in computation or in experiment. This approach leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The author explains why continuum analysis, computer simulations, and experiments form three entirely distinct approaches to chaos theory. In the end, 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 incomputations or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed. This algorithmic approach to chaos, dynamics and fractals will be of great interest to graduate students, research workers and advanced undergraduates in physics, engineering and other sciences with an interest in nonlinear science.

Details zur Ausgabe

• Verlag: Cambridge University Press
• Erscheinungsdatum: 2010
• ISBN 10: 0521467470
• ISBN 13: 9780521467476
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 348
• Kontakt zum Hersteller: Nicht verfügbar