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Mathematics 2006 - Dynamical Systems
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Edward Ott, University of Maryland, College Park
In the new edition of this classic textbook Ed 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.
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Paul Glendinning, University of Cambridge
By providing an introduction to nonlinear differential equations, Dr. Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations. His approach is readable and covers material both old and new to undergraduate courses. Included are treatments of the Poincaré-Bendixson theorem, the Hopf bifurcation and chaotic systems.
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John Banks, La Trobe University, Victoria
Valentina Dragan, La Trobe University, Victoria
Arthur Jones, La Trobe University, Victoria
This text presents concepts on chaos in discrete time dynamics that are accessible to anyone who has taken a first course in undergraduate calculus. Retaining its commitment to mathematical integrity, the book, originating in a popular one-semester middle level undergraduate course, constitutes the first elementary presentation of a traditionally advanced subject.
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James C. Robinson, University of Warwick
This introduction to ordinary differential and difference equations is suited not only for mathematicians but for scientists and engineers as well. Exact solutions methods and qualitative approaches are covered, and many illustrative examples are included. Matlab is used to generate graphical representations of solutions. Numerous exercises are featured and proved solutions are available for teachers.
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Boris Hasselblatt, Tufts University, Massachusetts
Anatole Katok, Pennsylvania State University
The theory of dynamical systems has given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introductory text covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. The only prerequisite is a basic undergraduate analysis course. The authors use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.
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Michael Brin, University of Maryland, College Park
Garrett Stuck, University of Maryland, College Park
This book provides a broad introduction to the subject of dynamical systems, suitable for a one or two-semester graduate course. In the first chapter, the authors introduce over a dozen examples, and then use these examples throughout the book to motivate and clarify the development of the theory. Topics include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics, one-dimensional dynamics, complex dynamics, and measure-theoretic entropy. The authors top off the presentation with some beautiful and remarkable applications of dynamical systems to areas such as number theory, data storage, and internet search engines.
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