| Description |
1 online resource (242 pages) |
| Series |
Understanding Complex Systems |
|
Springer complexity |
|
Understanding complex systems.
|
|
Springer complexity.
|
| Contents |
Intro -- Preface -- Contents -- 1 The Phenomenon of Chaos -- 1.1 Introduction -- 1.2 History of the Phenomenon Nowadays Labelled ̀Chaos' -- 1.3 The Re-injection Principle -- 1.4 The Taffy-Pulling Machine -- References -- 2 Simple Chaos -- 2.1 An Equation for Chaos -- 2.2 Robustness -- 2.3 A Prototype Example for Spiral Chaos -- 2.4 A Second Main Equation -- 2.5 Two Special Cases -- 2.6 Screw-Type Chaos -- 2.7 An Example with an Explicit Cross Section -- 2.8 A Two-Dimensional Embedding -- References -- 3 The Lorenzian Paradigm -- 3.1 Lorenz Chaos -- 3.2 An Analogue to the Lorenz Equation |
|
3.3 Two Internal Blue-Sky Catrastrophes -- 3.4 A Twin System -- 3.5 Understanding Lorenzian Flows -- 3.6 A Lorenzian Flow Arising Under Less Symmetric Conditions -- References -- 4 Hyperchaos -- 4.1 An Equation for ̀Hyperchaos' -- 4.2 Hyper Chaos-An Explicit Example -- References -- 5 The Gluing-Together Principle -- 5.1 Chaos in Single-Loop Feedback Systems -- References -- 6 Chaos in Toroidal Systems -- 6.1 The Bonhoeffer-Van der Pol Equation -- 6.2 Chaos in the Bonhoeffer-Van der Pol Equation -- 6.3 A Related Prototype -- 6.4 An Autonomous ̀One-Liner' -- 6.5 Higher-Order Toroidal Chaos |
|
6.6 Near-quasi-Periodic Chaos -- 6.7 The ̀Bracelet' Hypothesis -- References -- 7 Chaos and Reality -- 7.1 Some Everyday Examples -- 7.2 Towards a Definition of Chaos -- 7.3 Homoclinic Point Implies Chaos -- 7.4 Chaos and Hyperbolic Attractors -- References -- 8 Maps -- 8.1 Chaos and Structural Stability -- 8.2 The Baker's Transformation -- 8.3 A Toroidal Analogue -- References -- 9 Non-sink Attractors -- 9.1 The Anaxagoras Conjecture -- 9.2 An Ideal Chaotic Attractor ... -- 9.3 ... Is a Non-sink Attractor -- 9.4 A Philosophical Implication -- 9.5 The Lorenz Attractor as a Non-sink Attractor |
|
12.3 Lyapunov Characteristic Exponents -- References -- 13 Some Open Problems -- 13.1 Spectral Properties of Chaos -- 13.2 Chaos and Linear Systems -- 13.3 Chaos and Finite State Machines -- 13.4 Chaos in Non-point Systems -- 13.5 A Speculation -- References -- Appendix A A Psychological Astrologically Oriented Portrait -- A.1 Astrology: A Brief Introduction -- A.2 A Sketch of Otto Rössler's Personality -- Appendix B An Updated Hierarchy of Chaos -- B.1 Introduction -- B.2 Two-Dimensional Oscillators -- B.3 Quasi-periodic Regimes and Toroidal Chaos -- B.4 Dissipative Chaos |
| Summary |
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 |
| Bibliography |
References-10 Chaos and Turbulence-10.1 Three Higher-Order Baker's Transformations-10.2 Space-Filling, Big and Small-10.3 ̀Maximal Chaos'-10.4 Turbulence in Its Own Right-10.5 Turbulence and Coupled Oscillators-10.6 Coupled Oscillators and Boiling-10.7 An ̀Ideal' Example-10.8 A Smooth Example-10.9 A Hierarchy in Boiling-Type Turbulence-References-11 When to Expect Chaos-11.1 Suspecting Chaos-11.2 Two Exceptional Classes-11.3 Mass-Action Type Chaos-References-12 How to Prove Chaos-12.1 Looking at Maps-12.2 Looking at More Complicated Maps |
| Notes |
B.5 New Features Allowed by a Fourth Dimension |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from digital title page (viewed on June 04, 2020) |
| Subject |
Chaotic behavior in systems.
|
|
Chaotic behavior in systems
|
| Genre/Form |
Electronic books
|
| Form |
Electronic book
|
| Author |
Letellier, Christophe.
|
| ISBN |
9783030443054 |
|
3030443051 |
|
