An introduction to chaotic dynamics :classical and quantum /

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"Version: 20250501"--Title page verso.Includes bibliographical references.1. Preliminaries -- 1.1 Randomness -- 1.2. Uncertainty -- 1.3. Determinism -- 1.4. Dynamical systems -- 1.5. State space -- 1.6. Attractors -- 1.7. Nonlinear systems -- 1.8. Sensitive dependence -- 1.9. Models and faithfulness2. A brief history of chaotic dynamics -- 2.1. Sensitive dependence on initial conditions -- 2.2. Aperiodicity3. The phenomenology of chaotic dynamics -- 3.1. A simple example : the logistic map -- 3.2. A more complex example -- 3.3. Observations4. Dissipative chaos and strange attractors -- 4.1. Strange attractors -- 4.2. The Lorenz system -- 4.3. Prefractals versus fractals -- 4.4. Comparing dissipative and conservative chaotic systems5. Challenges for defining chaos -- 5.1. Qualitative considerations -- 5.2. Quantitative definitions of chaos -- 5.3. Counterexamples -- 5.4. Observations6. Implications for modeling and forecasting -- 6.1. Chaos in the actual world -- 6.2. Measurements, faithfulness, and the actual world -- 6.3. Numbers, computers, and modeling chaotic systems -- 6.4. Computers, integers, and memory -- 6.5. Shadowing -- 6.6. Machine learning7. Quantum influences on macroscopic chaotic systems -- 7.1. SDIC and quantum mechanics -- 7.2. Chaos and indeterminism in macroscopic systems I -- 7.3. Chaos and indeterminism in macroscopic systems II8. Quantum mechanics and quantum chaos -- 8.1. Defining quantum chaos -- 8.2. Semiclassical systems -- 8.3. Isolated quantum systems -- 8.4. Interacting systems -- 8.5. Quantum chaos and confusion9. Chaos and the classical-quantum relationship -- 9.1. Chaos and failure of the correspondence principle -- 9.2. Chaos and the failure of the false dilemma -- 9.3. Subtlety of the quantum-classical relationship -- 9.4. Contextual emergence and the validity of quantum mechanics10. Broader implications -- 10.1. Chaos in the world -- 10.2. Applications of chaos -- 10.3. Wider implications -- 10.4. ProspectsAppendix A. The chaotic hierarchy -- Appendix B. Topological entropy -- Appendix C. Global Lyapunov exponents.Full-text restricted to subscribers or individual document purchasers.Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. While the rules describing chaotic dynamical systems are well-specified and simple, the behaviour of many such systems is remarkably complex and produces output that appears random and for which long-term prediction is limited. The book begins by laying out preliminary material needed to understand the literature on chaos, providing the background that any reader would need to be able to navigate the literature. It goes on to discuss the history of the field, the different definitions of chaos and the implications of chaos for modelling phenomena and forecasting system behaviour before rounding out with broader implications.Introductory courses on chaos and/or nonlinear dynamics.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Robert C. Bishop is Professor of Physics and Philosophy and the John and Madeleine McIntyre Endowed Professor of Philosophy and History of Science in the Department of Physics and Engineering at Wheaton College. His research focuses on History and philosophy of physics and the social sciences and free will, with special attention to emergence, determinism, chaos, and complexity. He is author of Chaos Theory: A Quick Immersion (Tibidabo Publishing, 2023), and The Physics of Emergence Second Edition (Institute of Physics Press, 2024), and co-author of Emergence in Context: A Science-First Approach to Metaphysics (Oxford University Press, 2022).Title from PDF title page (viewed on June 2, 2025).

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: .,

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1 online resource (various pagings) :illustrations (some color).

Language

English

ISBN/ISSN

9780750364539

Classification

515.39

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Subject(s)

Dynamics.
Chaotic behavior in systems.
Chaos theory.
SCIENCE / Chaotic Behavior in Systems.

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Robert C. Bishop.

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