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Elementary Stability and Bifurcation Theory, 2nd Edition (Undergraduate Texts in Mathematics)by Gerard Iooss and Daniel D. Joseph
Synopses & ReviewsPublisher Comments:This substantially revised second edition teaches the bifurcation of asymptotic solutions to evolution problems governed by nonlinear differential equations. Written not just for mathematicians, it appeals to the widest audience of learners, including engineers, biologists, chemists, physicists and economists. For this reason, it uses only wellknown methods of classical analysis at foundation level, while the applications and examples are specially chosen to be as varied as possible.
Book News Annotation:(Advanced!) undergraduates and researchers with practical interest in the essentials and typical applications of bifurcation theory have for a decade been familiar with the first edition (1980) of this fine text. Drawing inspiration from Einstein's "everything should be made as simple as possible, but not simpler", the authors have undertaken simultaneously to simplify the treatment and to find room for discussion of some recent developments. Twelve chapters (many examples, many figures, no exercises) provide good coverage of the essentials of the asymptotics of (effectively) lowdimensional non linear differential equations of evolution. Applications notable for their variety. Handsomely produced. (NW)
Annotation c. Book News, Inc., Portland, OR (booknews.com) Synopsis:This substantially revised second edition teaches the bifurcation of asymptotic solutions to evolution problems governed by nonlinear differential equations. Written not just for mathematicians, it appeals to the widest audience of learners, including engineers, biologists, chemists, physicists and economists. For this reason, it uses only wellknown methods of classical analysis at foundation level, while the applications and examples are specially chosen to be as varied as possible.
Table of ContentsAsymptotic Solutions of Evolution Problems. Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension. Imperfection Theory and Isolated Solutions Which Perturb Bifurcation. Stability of Steady Solutions of Evolution Equations in Two Dimensions and n Dimensions. Appendices. Bifurcation of Steady Solution in Two Dimensions and the Stability of the Bifurcating Solutions. Appendix. Methods of Projection for General Problems of Bifurcation into Steady Solutions. Bifurcation of Periodic Solutions from Steady Ones (Hopf Bifurcation) in Two Dimensions. Bifurcation of Periodic Solutions in the General Case. Subharmonic Bifurcation of Forced TPeriodic Solutions. Bifurcation of Forced TPeriodic Solutions into Asymptotically QuasiPeriodic Solutions. Appendices. Secondary Subharmonic and Symptotically QuasiPeriodic Bifurcation of Periodic Solutions (of Hopf's Type) in the Autonomous Case. Stability and Bifurcation in Conservative Systems.
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Other books you might likeRelated SubjectsScience and Mathematics » Mathematics » Analysis General Science and Mathematics » Mathematics » Differential Equations Science and Mathematics » Mathematics » Probability and Statistics » General Science and Mathematics » Mathematics » Probability and Statistics » Statistics 

