Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics (Applied Mathematical Sciences) [Hardcover]

Andrzej Lasota (Author), Michael C. Mackey (Author)

Book Description

Publication Date: October 22, 1993 | ISBN-10: 0387940499 | ISBN-13: 978-0387940496 | Edition: 2nd

This book gives a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial-differential equations. Examples have been drawn from a variety of the sciences to illustrate the utility of the techniques presented. This material was organized and written to be accessible to scientists with knowledge of advanced calculus and differential equations. In various concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and chastic integrals and differential equations are introduced. The past few years have witnessed an explosive growth in interest in physical, biological, and economic systems that could be profitably studied using densities. Due to the general inaccessibility of the mathematical literature to the non-mathematician, there has been little diffusion of the concepts and techniques from ergodic theory into the study of these "chaotic" systems. This book intends to bridge that gap.

Editorial Reviews

Review

"This is a truly outstanding book. It is so well and carefully written that, despite the complexity of the subject matte and the difficulty of some of the mathematics, virtually everything is completely clear on a first reading. Indeed, the book is much more absorbing than most novels." Probability in the Engineering + Informational Sciences

Product Details

• Hardcover: 472 pages
• Publisher: Springer; 2nd edition (October 22, 1993)
• Language: English
• ISBN-10: 0387940499
• ISBN-13: 978-0387940496
• Product Dimensions: 9.3 x 6.2 x 1.2 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,401,557 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

10 of 11 people found the following review helpful:

5.0 out of 5 stars Excellent Book!, December 19, 2000

By 

John Stachurski (Melbourne, VIC Australia) - See all my reviews

This review is from: Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics (Applied Mathematical Sciences) (Hardcover)

This is one of my favorite maths books. My interest in it is not so much for the discussion of chaotic systems, but more for that on stochastically perturbed systems. As far as this topic goes, this is the best book I've found in the field by far. The treatment is careful and self-contained, and the proofs are clear throughout. Lots of intuition is given with each result.

As a caveat, note that the approach is based on analysis in general and functional analysis in particular. If you prefer probabilistic arguments look somewhere else.