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  • Reference work
  • © 2011

Mathematics of Complexity and Dynamical Systems

  • Provides an in-depth treatment of the study of mathematical complexity and dynamical systems
  • Presents theory, techniques and applications
  • Demonstrates how the behavior of an entire system is often more than the sum of its parts
  • Gathers together more than 100 mathematically-oriented, peer-reviewed entries from the 11-volume Encyclopedia of Complexity and Systems Science

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Table of contents (113 entries)

  1. Front Matter

    Pages I-XXIX
  2. Anomalous Diffusion on Fractal Networks

    • Igor M. Sokolov
    Pages 13-25
  3. Biological Fluid Dynamics, Non-linear Partial Differential Equations

    • Antonio DeSimone, François Alouges, Aline Lefebvre
    Pages 26-31
  4. Catastrophe Theory

    • Werner Sanns
    Pages 32-48
  5. Center Manifolds

    • George Osipenko
    Pages 48-62
  6. Chaos and Ergodic Theory

    • Jérôme Buzzi
    Pages 63-87
  7. Control of Non-linear Partial Differential Equations

    • Fatiha Alabau‐Boussouira, Piermarco Cannarsa
    Pages 102-125
  8. Discrete Control Systems

    • Taeyoung Lee, Melvin Leok, Harris McClamroch
    Pages 143-159
  9. Dynamics on Fractals

    • Raymond L. Orbach
    Pages 175-182
  10. Dynamics of Parametric Excitation

    • Alan Champneys
    Pages 183-204
  11. Entropy in Ergodic Theory

    • Jonathan L. F. King
    Pages 205-224
  12. Ergodicity and Mixing Properties

    • Anthony Quas
    Pages 225-240
  13. Ergodic Theorems

    • Andrés del Junco
    Pages 241-263
  14. Ergodic Theory: Basic Examples and Constructions

    • Matthew Nicol, Karl Petersen
    Pages 264-288
  15. Ergodic Theory : Fractal Geometry

    • Jörg Schmeling
    Pages 288-301

About this book

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics.  Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures.  These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic.
The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics.  Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Reviews

From the reviews:

“This remarkable collection comprises a selection of the more mathematically oriented articles from the enormous Encyclopedia of complexity and systems science. … The articles have been carefully edited … with a glossary of key terms, careful exposition, and a substantial specialised bibliography … . For a reasonably mathematically sophisticated reader, this will provide a good introduction to new areas, and the high quality of writing and editing means that one would be confident pointing researchers or undergraduates doing projects in related areas to this collection.” (Thomas B. Ward, Zentralblatt MATH, Vol. 1236, 2012)

Editors and Affiliations

  • RAMTECH LIMITED, Larkspur, USA

    Robert A. Meyers

About the editor

Dr. Meyers has more than 20 patents and 50 technical papers in the fields of photochemistry, pollution control, inorganic reactions, organic reactions, luminescence phenomena and polymers. He has published in primary literature journals including Science and the Journal of the American Chemical Society, and is listed in Who’s Who in America and Who’s Who in the World. Dr Meyers’ scientific achievements have been reviewed in feature articles in the popular press in publications such as The New York Times Science Supplement and The Wall Street Journal as well as more specialized publications such as Chemical Engineering and Coal Age. A public service film was produced by the Environmental Protection Agency of Dr. Meyers' chemical desulfurization invention for air pollution control.

Dr Meyers conceived and has served as Editor-in-Chief of the Academic Press (now Elsevier) Encyclopedia of Physical Science and Technology. This is an 18-volume publication of 780 twenty-page articles written to an audience of university students and practicing professionals. This encyclopedia, first published in 1987, was very successful, and because of this, was revised and reissued in 1992 as a second edition. The Third Edition was published in 2001 and is now on-line. Dr Meyers has completed two editions of the Encyclopedia of Molecular Cell Biology and Molecular Medicine for Wiley VCH publishers (1995 and 2004). These cover molecular and cellular level genetics, biochemistry, pharmacology, diseases and structure determination as well as cell biology. His eight-volume Encyclopedia of Environmental Analysis and Remediation was published in 1998 by John Wiley & Sons and his 15- volume Encyclopedia of Analytical Chemistry was published in 2000, also by John Wiley & Sons.

Dr. Meyers has worked with more than 20 Nobel laureates during his career.

Bibliographic Information

Buy it now

Buying options

eBook USD 600.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access