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About this book
About this book
Over the past two decades scientists, mathematicians, and engineers have come to understand that a large variety of systems exhibit complicated evolution with time. This complicated behavior is known as chaos. In the new edition of this classic textbook Edward Ott has added much new material and has significantly increased the number of homework problems. The most important change is the addition of a completely new chapter on control and synchronization of chaos. Other changes include new material on riddled basins of attraction, phase locking of globally coupled oscillators, fractal aspects of fluid advection by Lagrangian chaotic flows, magnetic dynamos, and strange nonchaotic attractors. This new edition will be of interest to advanced undergraduates and graduate students in science, engineering, and mathematics taking courses in chaotic dynamics, as well as to researchers in the subject.
Preface; 1. Introduction and overview; 2. One-dimensional maps; 3. Strange attractors and fractal dimensions; 4. Dynamical properties of chaotic systems; 5. Nonattracting chaotic sets; 6. Quasiperiodicity; 7. Chaos in Hamiltonian systems; 8. Chaotic transitions; 9. Multifractals; 10. Control and synchronization of chaos; 11. Quantum chaos.
Edward Ott is currently on the faculty of the University of Maryland where he holds the title of Distinguished University Professor of Physics and of Electrical and Computer Engineering. Before coming to Maryland in 1979, he was a Professor of Electrical Engineering at Cornell University (1968 1979). Prof. Ott's early research was on plasma physics and charged particle beams, including research on space plasmas, fusion plasmas, intense ion beams, and electromagnetic wave generation by electron beams. Since the early 1980s, Prof. Ott's main research interests have been in nonlinear dynamics and its applications to problems in science and engineering. Some of this work includes contributions in the areas of bifurcations of chaotic sets, the fractal dimension of strange attractors, the structure of basin boundaries, applications of chaotic dynamics to problems in fluids and plasmas, and the control and synchronization of chaos. Prof. Ott has also been active in the education of students in nonlinear dynamics. He is an author of over 300 research articles in scientific journals.
496 pages, 243 Line illus, 2 tabs
From reviews of the previous edition: '! a stimulating selection of topics that could be taught a la carte in postgraduate courses. The book is given unity by a preoccupation with scaling arguments, but covers almost all aspects of the subject (dimensions of strange attractors, transitions to chaos, thermodynamic formalism, scattering quantum chaos and so on ! Ott has managed to capture the beauty of this subject in a way that should motivate and inform the next generation of students in applied dynamical systems.' Nature From reviews of the previous edition: '! proves there is definitely enough worthwhile material on chaos to fill a semester ! Chapter exercises are at a good level for graduate students ! worthwhile for the researcher who wants to learn about chaos on his or her own ! a welcome volume for those who keep even modest collections on nonlinear dynamics.' Physics Today '! a book that will be of most interest to physicists and engineers ! The book is well written, and does contain material that is hard to find elsewhere. In particular, the discussion of fractal basin boundaries is lucidly written, and this is an important topic.' Bulletin of Mathematical Biology 'This second edition updates and expands the first edition. This very comprehensive book on chaotic dynamics is intended to use in a graduate course for scientists and engineers. It can also be used as a reference for researchers in the field of nonlinear dynamics.' Zentralblatt fur Mathematik 'The book is a comprehensive text and covrs all aspects of dynamical systems in a highly readable account.' Mathematics Today