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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Chaos, Dynamics, and Fractals - An Algorithmic Approach to Deterministic Chaos (Paperback, Revised)
Loot Price: R1,525
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Chaos, Dynamics, and Fractals - An Algorithmic Approach to Deterministic Chaos (Paperback, Revised)
Series: Cambridge Nonlinear Science Series
Expected to ship within 12 - 17 working days
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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.
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