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Chaos, Fractals, and Dynamics : Lecture Notes in Pure and Applied Mathematics - Fischer

Chaos, Fractals, and Dynamics

Lecture Notes in Pure and Applied Mathematics

By: Fischer

Paperback

Published: 1st June 1985
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This timely work focuses on the recent expansion of research in the field of dynamical systems theory with related studies of chaos and fractals. Integrating the work of leading mathematicians, physicists, chemists, and engineers, this research-level monograph discusses different aspects of the concepts of chaos and fractals from both experimental and theoretical points of view. Featuring the most recent advances-including findings made possible by the development of digital computers-this authoritative work provides thorough understanding of known behavior of nonlinear dynamical systems as well as considerable insight into complex aspects not yet well understood. With a broad, multidisciplinary perspective and an ample supply of literature citations, Chaos, Fractals, and Dynamics is an invaluable reference and starting point for further research for scientists in all fields utilizing dynamical systems theory, including applied mathematicians, physicists, dynamists, chemists, biomathematicians, and graduate students in these areas. Book jacket.

Prefacep. iii
Contributorsp. vii
Chaostrophes, Intermittency, and Noisep. 3
The Outstructure of the Lorenz Attractorp. 23
Chaos and Intermittency in an Endocrine System Modelp. 33
An Index for Chaotic Solutions in Cooperative Peelingp. 71
Unfoldings of Degenerate Bifurcationsp. 87
Example of an Axiom A ODEp. 105
Is There Chaos Without Noise?p. 117
Chaostrophes of Forced Van der Pol Systemsp. 123
Numerical Solution of the Lorenz Equations with Spatial Inhomogeneityp. 135
Some Results on Singular Delay-Differential Equationsp. 161
Feigenbaum Functional Equations as Dynamical Systemsp. 183
The Chaos of Dynamical Systemsp. 189
On Network Perturbations of Electrical Circuits and Singular Perturbation of Dynamical Systemsp. 197
On the Dynamics of Iterated Maps III: The Individual Molecules of the M-Set, Self-Similarity Properties, the Empirical n[superscript 2] Rule, and the n[superscript 2] Conjecturep. 213
On the Dynamics of Iterated Maps IV: The Notion of "Normalized Radical" R of the M-Set, and the Fractal Dimension of the Boundary of Rp. 225
On the Dynamics of Iterated Maps V: Conjecture That the Boundary of the M-Set Has a Fractal Dimension Equal to 2p. 235
On the Dynamics of Iterated Maps VI: Conjecture That Certain Julia Sets Include Smooth Componentsp. 239
On the Dynamics of Iterated Maps VII: Domain-Filling ("Peano") Sequences of Fractal Julia Sets, and an Intuitive Rationale for the Siegel Discsp. 243
Author Indexp. 255
Subject Indexp. 259
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780824773250
ISBN-10: 082477325X
Series: Lecture Notes in Pure and Applied Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 280
Published: 1st June 1985
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 27.9 x 21.6  x 1.4
Weight (kg): 0.5
Edition Number: 1