Global Bifurcation of Periodic Solutions with Symmetry

Global Bifurcation of Periodic Solutions with Symmetry
Author :
Publisher : Springer
Total Pages : 151
Release :
ISBN-10 : 9783540391500
ISBN-13 : 3540391509
Rating : 4/5 (509 Downloads)

Book Synopsis Global Bifurcation of Periodic Solutions with Symmetry by : Bernold Fiedler

Download or read book Global Bifurcation of Periodic Solutions with Symmetry written by Bernold Fiedler and published by Springer. This book was released on 2006-11-14 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


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