$Chaos bifurcations and fractals around us : a brief introduction /$

Chaos bifurcations and fractals around us : a brief introduction /

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Bibliographic Details
Author / Creator:	Szemplińska-Stupnicka, Wanda.
Imprint:	River Edge, NJ : World Scientific, ©2003.
Description:	1 online resource (v, 107 pages) : illustrations (some color)
Language:	English
Series:	World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 47 World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 47.
Subject:	Bifurcation theory. Chaotic behavior in systems. Differential equations, Nonlinear. Bifurcation theory. Chaotic behavior in systems. Differential equations, Nonlinear. Electronic book.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11137023

Hidden Bibliographic Details
ISBN:	9812564373 9789812564375 9789812386892 9812386890 9812386890
Notes:	Includes bibliographical references (pages 101-103) and index. Print version record.
Summary:	During the last twenty years, a large number of books on nonlinear chaotic dynamics in deterministic dynamical systems have appeared. These academic tomes are intended for graduate students and require a deep knowledge of comprehensive, advanced mathematics. There is a need for a book that is accessible to general readers, a book that makes it possible to get a good deal of knowledge about complex chaotic phenomena in nonlinear oscillators without deep mathematical study. Chaos, Bifurcations and Fractals Around Us: A Brief Introduction fills that gap. It is a very short monograph that, owing to geometric interpretation complete with computer color graphics, makes it easy to understand even very complex advanced concepts of chaotic dynamics. This invaluable publication is also addressed to lecturers in engineering departments who want to include selected nonlinear problems in full time courses on general mechanics, vibrations or physics so as to encourage their students to conduct further study.
Other form:	Print version: Szemplińska-Stupnicka, Wanda. Chaos bifurcations and fractals around us. River Edge, NJ : World Scientific, ©2003 9812386890

Table of Contents:

1. Introduction
2. Ueda's "strange attractors"
3. Pendulum. 3.1. Equation of motion, linear and weakly nonlinear oscillations. 3.2. Method of Poincaré map. 3.3. Stable and unstable periodic solutions. 3.4. Bifurcation diagrams. 3.5. Basins of attraction of coexisting attractors. 3.6. Global homoclinic bifurcation. 3.7. Persistent chaotic motion
chaotic attractor. 3.8. Cantor set
an example of a fractal geometric object
4. Vibrating system with two minima of potential energy. 4.1. Physical and mathematical model of the system. 4.2. The single potential well motion. 4.3. Melnikov criterion. 4.4. Fractal boundaries of basins of attraction and transient chaos in the region of principal resonance. 4.5. Oscillating chaos and unpredictability of the final state after destruction of the resonant attractor. 4.6. Boundary crisis of the oscillating chaotic attractor. 4.7. Persistent cross-well chaos. 4.8. Lyapunov exponents. 4.9. Intermittent transition to chaos. 4.10. Large orbit and the boundary crisis of the cross-well chaotic attractor. 4.11. Various types of attractors of the two-well potential system
5. Closing remarks.

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