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Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.

This remarkable reference covers topics such as quantum groups, Hopf Galois theory, actions and coactions of Hopf algebras, smash and crossed products, and the structure of cosemisimple Hopf algebras. ...

Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions....

0387129316An international summer course on Bifurcation Theory and Applications was held at Montecatini, Italy, June 24-July 2, 1983, organized by the CIME Foundation. The purpose was to feature the fundamental methods and the recent advances of the general theory, and to depict its role in approaching the analysis of natural phenomena. The importance of the connections between stability and bifurcation problems was constantly stressed. Thus the course also provided notions and results that complement previous courses organized by the CIME and other Italian summer schools on the subject of stability. ...

This second edition has been substantially revised. Its purpose is to teach the theory of bifurcation of asymptotic solutions of evolution problems governed by nonlinear differential equations. It is written not only for mathematicians, but for the broadest audience of potentially interested learners, including engineers, biologists, chemists, physicists and economists. For this reason, it uses only well-known methods of classical analysis at a foundation level. Applications and examples are stressed throughout, and these were chosen to be as varied as possible. ...

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Fundamentals of Stochastic Networks /by Oliver C. Ibe. n today's era of interdisciplinary studies and research activities, network models are becoming increasingly important in various areas where they have not regularly been used. Combining techniques from stochastic processes and graph theory to analyze the behavior of networks, Fundamentals of Stochastic Networks provides an interdisciplinary approach by including practical applications of these stochastic networks in various fields of study, from engineering and operations management to communications and the physical sciences.

DJVUA selection of Hiroshi Tanaka's brilliant works on stochastic processes and related topics. For researchers and graduate students in probability theory, analysis and mathematical physics. ...

The book gives an overview of path integral quantization and stochastic quantization of classical mechanics and field theory. The non-Abelian gauge field, the gravitational field, and the path integral representation of quantum statistical mechanics and stochastic quantization are described.