ENGLISH

Global Bifurcation of Periodic Solutions with Symmetry

By Bernold Fiedler (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1988
ISBN
9780387192345, 0-387-19234-4
DOI
10.1007/BFb0082943
LCC
QA3 .L28 no. 1309,QA372 .L28 no. 1309
Open Library ID
OL2036176M
Language
english
Format
DJVU
Filesize
1 MB (1210259 bytes)
Series
Lecture Notes in Mathematics 1309
Edition
1
Pages
154\152
Library
mexmat
Time added
2009-07-20 03:45:11
Analysis; Mathematical and Computational Physics

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.

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