Buch, Englisch, Band 1309, 154 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 260 g
Reihe: Lecture Notes in Mathematics
Buch, Englisch, Band 1309, 154 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 260 g
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-540-19234-3
Verlag: Springer Berlin Heidelberg
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
- Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
Weitere Infos & Material
Main results.- No symmetry — a survey.- Virtual symmetry.- Generic local theory.- Generic global theory.- General global theory.- Applications.- Discussion.- Appendix on genericity.
