Global bifurcation of periodic solutions with symmetry
Author(s)
Bibliographic Information
Global bifurcation of periodic solutions with symmetry
（Lecture notes in mathematics, 1309）
Springer-Verlag, c1988
- : gw
- : us
- Other Title
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Periodic solutions with symmetry
Available at / 82 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: gwL/N||LNM||13099788888400
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
: BerlinDC19:514.7/F4522070086072
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Note
Bibliography: p. [135]-140
Includes index
Description and Table of Contents
Description
This largely self-contained research monograph addresses the following type of questions. Suppose one encounters a continuous time dynamical system with some built-in symmetry. Should one expect periodic motions which somehow reflect this symmetry? And how would periodicity harmonize with symmetry? Probing into these questions leads from dynamics to topology, algebra, singularity theory, and to many applications. Within a global approach, the emphasis is on periodic motions far from equilibrium. Mathematical methods include bifurcation theory, transversality theory, and generic approximations. A new homotopy invariant is designed to study the global interdependence of symmetric periodic motions. Besides mathematical techniques, the book contains 5 largely nontechnical chapters. The first three outline the main questions, results and methods. A detailed discussion pursues theoretical consequences and open problems. Results are illustrated by a variety of applications including coupled oscillators and rotating waves: these links to such disciplines as theoretical biology, chemistry, fluid dynamics, physics and their engineering counterparts make the book directly accessible to a wider audience.
Table of Contents
Main results.- No symmetry - a survey.- Virtual symmetry.- Generic local theory.- Generic global theory.- General global theory.- Applications.- Discussion.- Appendix on genericity.
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