Nagashima / Baba Introduction to Chaos

Physics and Mathematics of Chaotic Phenomena
1. Auflage 2002
ISBN: 978-1-4200-5081-3
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 168 Seiten

Introduction to Chaos: Physics and Mathematics of Chaotic Phenomena focuses on explaining the fundamentals of the subject by studying examples from one-dimensional maps and simple differential equations. The book includes numerous line diagrams and computer graphics as well as problems and solutions to test readers' understanding.

The book is written primarily for advanced undergraduate students in science yet postgraduate students and researchers in mathematics, physics, and other areas of science will also find the book useful.

Zielgruppe

Advanced undergraduate students in science and engineering; postgraduate students and researchers in mathematics, physics, and other areas of science.

Autoren/Hrsg.

Nagashima, H

Baba, Y

Fachgebiete

• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Inhaltsverzeichnis

WHAT IS CHAOS?
Characteristics of chaos
Chaos in nature

LI-YORKE CHAOS, TOPOLOGICAL ENTROPY, AND LYAPUNOV NUMBER
Li-Yorke theorem and Sharkovski theorem: Li-Yorke's theorem Sharkovski's theorem
Periodic orbits: Number of periodic orbits
Stability of orbits
Li-Yorke theorem (continued)
Scrambled set and observability of Li-Yorke chaos: Nathanson's example
Observability of Li-Yorke chaos
Topological entropy
Density of orbits: Observable chaos and Lyapunov number
Denseness of orbits
Invariant measure
Lyapunov number
Summary

ROUTE TO CHAOS
Pitchfork bifurcation and Feigenbaum route
Conditions for pitchfork bifurcation
Windows
Intermittent chaos

CHAOS IN REALISTIC SYSTEMS
Conservative system and dissipative system
Attractors and Poincare section
Lyapunov numbers and change of volume
Construction of attractor
Hausdorff dimension, generalized dimension and fractal
Evaluation of correlation dimension
Evaluation of Lyapunov number
Global spectrum-the If(a) method

APPENDICES
Periodic solutions of the logistic map
Mobius function and inversion formula
Countable sets and uncountable sets
Upper limit and lower limit
Lebsgue measure
Normal numbers
Periodic orbits with finite fraction initial value
The delta-function
Where does period 3 window begin in logistic map?
Newton method
How to evaluate topological entropy
Examples of invariant measure
Generalized dimension Dq is monotonically decreasing in q
Saddle point method
Chaos in double-pendulum
Singular points and limit cycle of van der Pol Equation
Singular points of the Rossler model

REFERENCES
SOLUTIONS
INDEX