Introduction to Chaos: Physics and Mathematics of Chaotic Phenomena, 1st Edition (Paperback) book cover

Introduction to Chaos

Physics and Mathematics of Chaotic Phenomena, 1st Edition

By H Nagashima, Y Baba

CRC Press

168 pages | 261 B/W Illus.

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Paperback: 9780750305082
pub: 1998-01-01
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Description

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.

Reviews

"… the book provides an interesting account of the chaotic behaviour in dynamical systems … [it] certainly serves as a useful source of reference for postgraduate students and researchers."

-Mathematics Today

"The book by Nagashima and Baba seems to combine this wide perspective and at the same time enough precision to get real insight in what is going on … Altogether this is an interesting new introduction to nonlinear dynamics and will certainly be worthwhile to try it out for a mixed audience."

-Nonlinear Science Today

"… this may be the best technical undergraduate book on chaos theory on the market. Nagashima and Baba eschew fancy color illustrations and concentrate on the theory instead. The exposition is entirely mathematical, presented in clear, terse fashion with numerous crisp graphs. Some 46 problems (with solutions) help to deepen the reader's understanding of the material. The focus is on one-dimensional maps and simple differential equations; this rather narrow scope allows a depth of coverage not normally seen in a book at this level."

-Choice Magazine

Table of Contents

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

Subject Categories

BISAC Subject Codes/Headings:
MAT007000
MATHEMATICS / Differential Equations
SCI055000
SCIENCE / Physics