Chaos. (English) Zbl 0743.58005

Nonlinear Science: Theory and Applications. Manchester: Manchester University Press,. 324 p. (1986).

Contents: Part I. Prologue.
1. ‘What is the use of chaos?’ by M. Conrad, pp. 3-14, 2. ‘A graphical zoo of strange and peculiar attractors’ by A. V. Holden and M. A. Muhamad, pp. 15-35.
Part II. Iterations.
3. ‘One-dimensional iterative maps’ by H. A. Lauwerier, pp. 39-57, 4. ‘Two-dimensional iterative maps’ by H. A. Lauwerier, pp. 58- 95.
Part III. Endogenous chaos.
5. ‘Chaos in feedback systems’ by A. Mees, pp. 99-110, 6. ‘The Lorenz equations’ by C. Sparrow, pp. 111-134, 7. ‘Instabilities and chaos in lasers and optical resonators’ by W. J. Firth, pp. 135- 157, 8. ‘Differential systems in ecology and epidemiology’ by W. M. Schaffer and M. Kot, pp. 158-178, 9. ‘Oscillations and chaos in cellular metabolism and physiological systems’ by P. E. Rapp, pp. 179-208.
Part IV. Forced chaos.
10. ‘Periodically forced nonlinear oscillators’ by K. Tomita, pp. 211-236, 11. ‘Chaotic cardiac rhythms’ by L. Glass, A. Shrier and J. Bélair, pp. 237-256, 12. ‘Chaotic oscillations and bifurcations in squid giant axons’ by K. Aihara and G. Matsumoto, pp. 257-269.
Part V. Measuring chaos.
13. ‘Quantifying chaos with Lyapunov exponents’ by A. Wolf, pp. 273-290, 14. ‘Estimating the fractal dimensions and entropies of strange attractors’ by P. Grassberger, pp. 291-311.
Part VI. Epilogue.
15. ‘How chaotic is the universe?’ by O. E. Rössler, pp. 315- 320.
Index, pp. 321-324.

MSC:

58-06	Proceedings, conferences, collections, etc. pertaining to global analysis
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
00B25	Proceedings of conferences of miscellaneous specific interest
37B99	Topological dynamics
37E99	Low-dimensional dynamical systems
37C70	Attractors and repellers of smooth dynamical systems and their topological structure
78A60	Lasers, masers, optical bistability, nonlinear optics
92-XX	Biology and other natural sciences
58Z05	Applications of global analysis to the sciences

Keywords:

Chaos; entropy; chaos; attractors; one-dimensional iterative maps; two-dimensional iterative maps; Lorenz equations; lasers; optical resonators; ecology; epidemiology; cellular metabolism; physiological systems; nonlinear oscillators; cardiac rhythms; squid giant axons; Lyapunov exponents; fractal dimensions; universe