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  • © 2020

Chaos

The World of Nonperiodic Oscillations

  • Authored by one of the pioneers of chaos theory, revealed for the first time

  • Provides many original insights into chaos theory

  • Contains many unpublished examples and discussions

Part of the book series: Understanding Complex Systems (UCS)

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eBook USD 119.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-44305-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 159.99
Price excludes VAT (USA)
Hardcover Book USD 159.99
Price excludes VAT (USA)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xv
  2. The Phenomenon of Chaos

    • Otto E. Rössler, Christophe Letellier
    Pages 1-11
  3. Simple Chaos

    • Otto E. Rössler, Christophe Letellier
    Pages 13-36
  4. The Lorenzian Paradigm

    • Otto E. Rössler, Christophe Letellier
    Pages 37-54
  5. Hyperchaos

    • Otto E. Rössler, Christophe Letellier
    Pages 55-62
  6. The Gluing-Together Principle

    • Otto E. Rössler, Christophe Letellier
    Pages 63-66
  7. Chaos in Toroidal Systems

    • Otto E. Rössler, Christophe Letellier
    Pages 67-89
  8. Chaos and Reality

    • Otto E. Rössler, Christophe Letellier
    Pages 91-106
  9. Maps

    • Otto E. Rössler, Christophe Letellier
    Pages 107-116
  10. Non-sink Attractors

    • Otto E. Rössler, Christophe Letellier
    Pages 117-125
  11. Chaos and Turbulence

    • Otto E. Rössler, Christophe Letellier
    Pages 127-143
  12. When to Expect Chaos

    • Otto E. Rössler, Christophe Letellier
    Pages 145-150
  13. How to Prove Chaos

    • Otto E. Rössler, Christophe Letellier
    Pages 151-156
  14. Some Open Problems

    • Otto E. Rössler, Christophe Letellier
    Pages 157-160
  15. Back Matter

    Pages 161-234

About this book

Written in the 1980s by one of the fathers of chaos theory, Otto E. Rössler, the manuscript presented in this volume eventually never got published. Almost 40 years later, it remains astonishingly at the forefront of knowledge about chaos theory and many of the examples discussed have never been published elsewhere. 
The manuscript has now been edited by Christophe Letellier - involved in chaos theory for almost three decades himself, as well as being active in the history of sciences - with a minimum of changes to the original text.
Finally released for the benefit of specialists and non-specialists alike, this book is equally interesting from the historical and the scientific points of view: an unconventionally modern approach to chaos theory, it can be read as a classic introduction and short monograph as well as a collection of original insights into advanced topics from this field.

Keywords

  • Chaotic attractors
  • Topology of chaos
  • Rössler attractor
  • Bonhoeffer-van der Pol equation
  • Hyperchaos
  • Otto Rössler
  • complexity

Authors and Affiliations

  • Faculty of Science, University of Tübingen, Tübingen, Germany

    Otto E. Rössler

  • Normandie University - CORIA, Saint-Etienne du Rouvray, France

    Christophe Letellier

About the authors

Otto E. Rössler has a background in electronics (due to his radio-amateur experience during his teenage years) and got a first doctorate in medicine. Then he progressively turned to theoretical chemistry after two post-doc positions in behavioral biology (with Konrad Lorenz in Seewiesen) and in theoretical biology (with Robert Rosen at Buffalo).

He started his career in performing numerical simulations of chemical reaction models with the help of an analog computer. He spent nearly a decade focusing on chaotic attractors. He proposed the so-called Rössler system and introduced the concept of hyperchaos.

The Rössler system is today the second-most quoted system in chaos theory (after the Lorenz one). This program more or less ended with his proposition for a hierarchy of chaos, for which he proposed many different examples of various types of chaos.

With his numerous contributions, he largely contributed to construct the paradigm of chaos, insisting on the qualitative approach inherited from Henri Poincaré.

This book, written in the early 1980s, is a kind of review of his views on this topic. He then switched to researches in biogenesis, endophysics, cryodynamics, etc. He wrote many hundreds of scientific papers.



Christophe Letellier has a background in physics. He concluded his Ph.D. in chaos theory on data-driven modelling and topological characterization of chaotic attractors.

With Robert Gilmore (Drexel University, U.S.A.) he investigated the role of symmetries in dynamical systems.

Together with Luis Aguirre (Universidade Federal de Minas Gerais, Brazil), he developed the observability coefficients for assessing the quality of information contained in a measured variable.

For 20 years, he also collaborated with physicians to transfer techniques from chaos theory towards clinical applications in mechanical ventilation, heart variability and oncology.

With Fabrice Denis, he developed a clinical follow-up method for patients who were treated for lung cancer.

Since 15 years he teaches a course in history of science and wrote a book, entitled Chaos in Nature, exploring how chaos emerged in the 20th century.

Bibliographic Information

Buying options

eBook USD 119.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-44305-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 159.99
Price excludes VAT (USA)
Hardcover Book USD 159.99
Price excludes VAT (USA)