Some popular accounts of the history and folklore of nonlinear dynamics
and chaos include:
A. Fisher, Chaos: The ultimate asymmetry, MOSAIC 16 (1),
pp. 24-33 (January/February 1985).
J. P. Crutchfield, J. D. Farmer, N. H. Packard, and R. S.\
Shaw, Chaos, Sci. Am. 255 (6), pp. 46-57 (1986).
J. Gleick, Chaos: Making a new science
(Viking: New York, 1987).
I. Stewart, Does god play dice? The mathematics of chaos
(Basil Blackwell: Cambridge, MA, 1989).
The following books are helpful references for some of the
material covered in this book:
R. Abraham and C. Shaw, Dynamics--The geometry of
behavior, Vol. 1-4 (Aerial Press: Santa Cruz, CA, 1988).
D. K. Arrowsmith and C. M. Place, An introduction to
dynamical systems (Cambridge University Press: New York, 1990).
G. L. Baker and J. P. Gollub, Chaotic dynamics (Cambridge University Press: New
York, 1990).
P. Bergé, Y. Pomeau, and C. Vidal, Order within chaos
(John Wiley: New York, 1984).
R. L. Devaney, An introduction to chaotic dynamical
systems, second ed.
(Addison-Wesley: New York, 1989).
E. A. Jackson, Perspectives of nonlinear dynamics, Vol. 1-2
(Cambridge
University Press: New York, 1990).
F. Moon, Chaotic vibrations (John
Wiley: New York, 1987).
J. Thompson and H. Stewart, Nonlinear
dynamics and chaos (John Wiley: New York, 1986).
S. Rasband,
Chaotic dynamics of nonlinear systems (John Wiley: New York, 1990).
S. Wiggins, Introduction to applied nonlinear dynamical
systems and chaos (Springer-Verlag: New York, 1990).
These review articles provide a quick introduction to the current research
problems and methods of nonlinear dynamics:
J.-P. Eckmann, Roads to turbulence in dissipative dynamical
systems, Rev. Mod. Phys. 53 (4), pp. 643-654 (1981).
J.-P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange
attractors, Rev. Mod. Phys. 57 (3), pp. 617-656 (1985).
C. Grebogi, E. Ott, and J.\
Yorke, Chaos, strange attractors, and fractal basin boundaries in nonlinear
dynamics, Science 238, pp. 632-638 (1987).
E. Ott, Strange attractors and chaotic motions of dynamical
systems, Rev. Mod. Phys. 53 (4), pp. 655-671 (1981).
T. Parker
and L. Chua, Chaos: A tutorial for engineers, Proc. IEEE 75 (8),
pp. 982-1008 (1987).
R. Shaw, Strange attractors, chaotic
behavior, and information flow, Z. Naturforsch. 36a, pp.
80-112 (1981).
Advanced theoretical results are described in the following books:
V. I. Arnold, Geometrical methods in the theory of
ordinary differential equations, second ed. (Springer-Verlag: New
York, 1988).
J. Guckenheimer and P. Holmes, Nonlinear oscillations,
dynamical systems, and bifurcations of vector fields, second printing
(Springer-Verlag: New York, 1986).
D. Ruelle, Elements of differentiable dynamics and
bifurcation theory (Academic Press: New York, 1989).
S. Wiggins, Global bifurcations and chaos
(Springer-Verlag: New York, 1988).