Global Bifurcation of Periodic Solutions with Symmetry / by Bernold Fiedler.

Format:

Book

Author/Creator:

Fiedler, Bernold, 1956- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1309.

Lecture Notes in Mathematics, 0075-8434 ; 1309

Language:

English

Subjects (All):

Global analysis (Mathematics).

Analysis.

Theoretical, Mathematical and Computational Physics.

Local Subjects:

Analysis.

Theoretical, Mathematical and Computational Physics.

Physical Description:

1 online resource (X, 154 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1988.

System Details:

text file PDF

Summary:

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.

Contents:

Main results

No symmetry - a survey

Virtual symmetry

Generic local theory

Generic global theory

General global theory

Applications

Discussion

Appendix on genericity.

Other Format:

Printed edition:

ISBN:

9783540391500

Access Restriction:

Restricted for use by site license.