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Chaotic behavior in systems --- Differentiable dynamical systems

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This by now classic text provides an excellent introduction to and survey of the still-expanding field of quantum chaos. For this long-awaited fourth edition, the original text has been thoroughly modernized. The topics include a brief introduction to classical Hamiltonian chaos, a detailed exploration of the quantum aspects of nonlinear dynamics, quantum criteria used to distinguish regular and irregular motion, and antiunitary (generalized time reversal) and unitary symmetries. The standard Wigner-Dyson symmetry classes, as well as the non-standard ones introduced by Altland and Zirnbauer, are investigated and illustrated with numerous examples. Random matrix theory is presented in terms of both classic methods and the supersymmetric sigma model. The power of the latter method is revealed by applications outside random-matrix theory, such as to quantum localization, quantum graphs, and universal spectral fluctuations of individual chaotic dynamics. The equivalence of the sigma model and Gutzwiller’s semiclassical periodic-orbit theory is demonstrated. Last but not least, the quantum mechanics of dissipative chaotic systems are also briefly described. Each chapter is accompanied by a selection of problems that will help newcomers test and deepen their understanding, and gain a firm command of the methods presented.

Quantum chaos. --- Chaos, Quantum --- Chaotic behavior in systems --- Quantum theory --- Quantum theory. --- Statistical physics. --- Mathematical physics. --- Quantum Physics. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Statistical Physics and Dynamical Systems. --- Mathematical Methods in Physics. --- Physical mathematics --- Physics --- Mathematical statistics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Mathematics --- Statistical methods --- Quantum physics. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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The book presents nonlinear, chaotic and fractional dynamics, complex systems and networks, together with cutting-edge research on related topics. The fifteen chapters – written by leading scientists working in the areas of nonlinear, chaotic and fractional dynamics, as well as complex systems and networks – offer an extensive overview of cutting-edge research on a range of topics, including fundamental and applied research. These include but are not limited to aspects of synchronization in complex dynamical systems, universality features in systems with specific fractional dynamics, and chaotic scattering. As such, the book provides an excellent and timely snapshot of the current state of research, blending the insights and experiences of many prominent researchers.

Physics. --- Complexity, Computational. --- Vibration. --- Dynamical systems. --- Dynamics. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Vibration, Dynamical Systems, Control. --- Statistical Physics and Dynamical Systems. --- Complexity. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Cycles --- Sound --- Complexity, Computational --- Electronic data processing --- Machine theory --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Statistical physics. --- Engineering. --- Construction --- Industrial arts --- Technology --- Mathematical statistics --- Statistical methods --- Computational complexity. --- Chaotic behavior in systems. --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Thermodynamics --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Nonlinear theories --- System theory

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This book covers the proceedings from the 2016 International Symposium on Chaos, Complexity and Leadership, and reflects current research results of chaos and complexity studies and their applications in various fields. Included are research papers in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of chaos and complex systems. Also discussed are leadership and management applications of chaos and complexity theory.

Chaotic behavior in systems. --- Business. --- Computer simulation. --- Economic theory. --- Business and Management. --- Operations Research/Decision Theory. --- Simulation and Modeling. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Economic theory --- Political economy --- Social sciences --- Economic man --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Trade --- Economics --- Management --- Commerce --- Industrial management --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory --- Operations research. --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- Decision making. --- Statistical physics. --- Physics --- Mathematical statistics --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Problem solving --- Statistical methods --- Decision making