Chaos : the world of nonperiodic oscillations /: the world of nonperiodic oscillations. ([2020])

• Record Type: Book
• Further Information: Note: Otto E. Rössler, Christophe Letellier.
• Other Names: Rössler, Otto E; Letellier, Christophe
• 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
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource
• Subjects: 003.857; 621; Chaotic behavior in systems; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030443054; 3030443051
• Related ISBNs: 9783030443047
• Notes: Note: 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; Note: Includes bibliographical references and index.; Note: Description based on online resource; title from digital title page (viewed on June 04, 2020).
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