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基本説明
A graduate textbook in dynamical systems theory and mathematical physics and by researchers in applied mathematics and mathematical physics.
Full Description
Why have scientists, engineers, and mathematicians become intrigued by chaos? Chaos is about predictability in even the most unstable systems, and symmetry is a pattern of predictability - a conceptual tool to help understand complex behaviour. The Symmetry of Chaos treats this interplay between chaos and symmetry. This graduate textbook in physics, applied mathematics, engineering, fluid dynamics, and chemistry is full of exciting new material, illustrated by hundreds of figures. Nonlinear dynamics and chaos are relatively young fields, an in addition to serving textbook markets, there is a strong interest among researchers in new results in the field.
Contents
Part I
Examples and Simple Application
1: Introduction
2: Simple Symmetries
3: Image Dynamical Systems
4: Covers
5: Peeling Bifurcations
6: Three-Fold and Four-Fold covers
7: Multichannel Intermittency
8: Driven Two-Dimensional Dynamical Systems
9: Larger Symmetries
Part II
Mathematical Foundations
10: Group Theory Basics
11: Invariant Polynomials
12: Equivariant Dynamics in R N
13: Covering Dynamical Systems
14: Symmetries Due to Symmetry
Part III
Symmetry without Groups: Topology
15: symmetry without Groups: "Topological Symmetry"
16: All the Covers of the Horsehoe
Appendix A A Potpourri of Equivariant Systems
References
Index
