Chaos, Fractals, and Dynamics
This book contains eighteen papers, all more-or-less linked to the theory of dynamical systems together with related studies of chaos and fractals. It shows many fractal configurations that were generated by computer calculations of underlying two-dimensional maps.
Table of Contents
Part I 1. Chaostrophes, Incermittency, and Noise 2. The Outstructure of the Lorenz Attractor 3. Chaos and Intermittency in an Endocrine System Model 4. An Index for Chaotic Solutions in Cooperative Peeling 5. Unfoldings of Degenerate Bifurcations 6. Example of an Axiom a ODE Part II 7. Is There Chaos Without Noise? 8. Chaostrophes of Forced Van der Pol Systems 9. Numerical Solution of the Lorenz Equations with Spatial Inhomogeneity 10. Some Results on Singular Delay—Differential Equations 11. Feigenbaum Functional Equations as Dynamical Systems 12. The Chaos of Dynamical Systems 13. On Network Perturbations of Electrical Circuits and Singular Perturbation of Dynamical Systems 14. On the Dynamics of Iterated Maps III: The Individual Molecules of the M—Set, Self—Similarity Properties, the Empirical n2 Rule, and the n2 Conjecture 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 16. On the Dynamics of Iterated Maps V: Conjecture That the Boundary of the H—Set Has a Fractal Dimension Equal to 2 17. On the Dynamics of Iterated Maps VI: Conjecture That Certain Julia Sets Include Smooth Components 18. On the Dynamics of Iterated Maps VII: Domain—Filling (“Peamo”) Sequemces of Fractal Julia Sets, and an Intuitive Rationale for the Siegel Discs