Chaos, fractals, and dynamics / edited by P. Fischer, William R. Smith.

Format:

Book

Contributor:

Fischer, P., 1940-

Smith, William R. (William Robert), 1943-

Series:

Lecture notes in pure and applied mathematics ; v. 98.

Lecture notes in pure and applied mathematics ; v. 98

Language:

English

Subjects (All):

Differentiable dynamical systems.

Chaotic behavior in systems.

Fractals.

Physical Description:

viii, 261 pages : illustrations ; 25 cm.

Place of Publication:

New York : M. Dekker, [1985]

Summary:

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.

Contents:

1. Chaostrophes, Intermittency, and Noise / Ralph H. Abraham 3

2. The Outstructure of the Lorenz Attractor / Ralph H. Abraham, Christopher C. Shaw 23

3. Chaos and Intermittency in an Endocrine System Model / Ralph H. Abraham, Huseyin Kocak, William R. Smith 33

4. An Index for Chaotic Solutions in Cooperative Peeling / Okan Gurel 71

5. Unfoldings of Degenerate Bifurcations / W. F. Langford 87

6. Example of an Axiom A ODE / Otto E. Rossler 105

7. Is There Chaos Without Noise? / Ralph H. Abraham 117

8. Chaostrophes of Forced Van der Pol Systems / Ralph H. Abraham, Katherine A. Scott 123

9. Numerical Solution of the Lorenz Equations with Spatial Inhomogeneity / M. E. Alexander, J. Brindley, I. M. Moroz 135

10. Some Results on Singular Delay-Differential Equations / Shui-Nee Chow, David Green, Jr. 161

11. Feigenbaum Functional Equations as Dynamical Systems / P. Fischer 183

12. The Chaos of Dynamical Systems / Morris W. Hirsch 189

13. On Network Perturbations of Electrical Circuits and Singular Perturbation of Dynamical Systems / Giko Ikegami 197

14. 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] Conjecture / Benoit B. Mandelbrot 213

15. 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 R / Benoit B. Mandelbrot 225

16. On the Dynamics of Iterated Maps V: Conjecture That the Boundary of the M-Set Has a Fractal Dimension Equal to 2 / Benoit B. Mandelbrot 235

17. On the Dynamics of Iterated Maps VI: Conjecture That Certain Julia Sets Include Smooth Components / Benoit B. Mandelbrot 239

18. On the Dynamics of Iterated Maps VII: Domain-Filling ("Peano") Sequences of Fractal Julia Sets, and an Intuitive Rationale for the Siegel Discs / Benoit B. Mandelbrot 243.

Notes:

Includes bibliographies and indexes.

ISBN:

082477325X

OCLC:

11865773