Bibliography

Version of 18Sep92

R. Abraham and C. Shaw, 1982.  Dynamics, the Geometry of Behavior.  Reading, Massachusetts:  Benjamin Cummings.

V.I. Arnol'd, 1973.  Ordinary Differential Equations, translated and edited by R.A. Silverman.  Cambridge, Mass.: MIT Press.

V.I. Arnol'd, 1980.  Mathematical Methods of Classical Mechanics, translated by K. Vogtmann and A. Weinstein.  New York, Berlin, Heidelberg, and Tokyo:  Springer-Verlag.

V.I. Arnol'd and A. Avez, 1968.  Ergodic Problems of Classical Mechanics.  New York and Amsterdam:  Benjamin.

D.K. Arrowsmith and C.M. Place, 1990.  An Introduction to Dynamical Systems.  Cambridge and New York:  Cambridge U. Press.  

G.L. Baker and J.P. Gollub, 1990.  Chaotic Dynamics, and Introduction.  Cambridge and New York:  Cambridge U. Press.

M.F. Barnsley, 1988. Fractals Everywhere .  New York:  Academic.

G.D. Birkhoff, 1927.  Dynamical Systems, Amer. Math. Soc. Colloquium Publ. 9.  Providence:  American Mathematical Society.

S.G. Brush, 1970.  Boltzmann, Ludwig,  pp. 260-268 in the Dictionary of Scientific Biography, vol. II, C.C. Gillispie, ed.  New York:  Charles Scribner's Sons.

B.V. Chirikov, 1979.  A universal Instability of Many Dimensional Oscillator Systems.  Phys. Rep.  52, 263-379.

S.-N. Chow and J.K. Hale, 1982.  Methods of Bifurcation Theory.  New York, Berlin, Heidelberg, and Tokyo:  Springer-Verlag.

E.A. Coddington and N. Levinson, 1955.  Theory of Ordinary Differential Equations.  New York:  McGraw-Hill.

J.D. Crawford, 1991.  Introduction to Bifurcation Theory.  Reviews of Modern Physics  63, 991-1037.  (Available from the American Institute of Physics, Reprints Department, 335 E. 45th St., New York  NY  10017 for $9.00.  Specify Reprint number 395.)

P. Cvitanovic, ed., 1989.  Universality in Chaos.  Bristol, IOP Publishing.

R.L. Devaney, 1986.  Introduction to Chaotic Dynamical Systems.  Menlo Park, Calif.:  Benjamin-Cummings.

J. Dieudonné, 1975.  Poincaré, Jules Henri,  pp. 51-61 in the Dictionary of Scientific Biography, vol. XI, C.C. Gillispie, ed.  New York:  Charles Scribner's Sons.

J.-P. Eckmann and D. RUELLE, 1985.  Ergodic Theory of Chaos and Strange Attractors.  Reviews of Modern Physics  57, 617-656.  (Available from the American Institute of Physics, Reprints Department, 335 E. 45th St., New York  NY  10017 for $9.00.  Specify Reprint number 258.)

K.J. Falconer, 1965.  The Geometry of Fractal Sets.  Cambridge:  Cambridge University Press.

M. Feigenbaum, 1978.  Quantitative Universality for a Class of Nonlinear Transformations.  J. Stat. Phys. 19, 25- 52.

H. Furstenberg, 1981.  Recurrence in Ergodic Theory and Combinatorial Number Theory.  Princeton:  Princeton Univ. Press.

J. Gleick, 1987.  Chaos:  Making a New Science.  New York:  Viking, 1987.

M. GOLUBITSKY and D.G. SCHAEFFER, 1984.  Singularities and Groups in Bifurcation Theory.  Berlin, Heidelberg, Tokyo, and New York:  Springer-Verlag.

C. Grebogi, E. Ott, S. Pelikan, and J.A. Yorke, 1984.  Strange Attractors that are Not Chaotic.  Physica  13D, 261-268.

J. GUCKENHEIMER and P. HOLMES, 1983.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields.  Applied Mathematical Sciences  42.  New York, Berlin, Heidelberg, and Tokyo:  Springer-Verlag.

J.K. Hale, 1977.  Ordinary Differential Equations, 2nd ed.  Huntington, New York:  R.E. Krieger.

J.K. Hale and H. Koçak, 1989.  Differential Equations:  An Introduction to Dynamics and Bifurcations .  New York, Berlin, Heidelberg, and Tokyo:  Springer-Verlag, to appear.

P.R.  Halmos, 1950.  Measure Theory.  New York: Van Nostrand.  (Now published by Springer-Verlag.)

P. Hartman, 1973.  O.D.E.   Baltimore: Hartman.

D.R. Hofstadter, 1980.  Gödel, Escher, Bach:  An Eternal Golden Braid.  New York:  Vintage Books.

D.W. Jordan and P. Smith, 1987.  Nonlinear Ordinary Differential Equations  (second edition).  Oxford: Clarendon Press.
  
A.N. Kolmogorov and S.V. Fomin, 1970.  Introductory Real Analysis, translated and edited by R.A. Silverman.  New York:  Dover.

S. Lefschetz, 1963.  Differential Equations, Geometric Theory.  New York:  Interscience (currently reprinted by Dover).

A.J. Lichtenberg and M.A. Lieberman, 1982.  Regular and Stochastic Motion.  New York, Berlin, Heidelberg, and Tokyo:  Springer-Verlag.

B-L. HAO, 1984.  Chaos .  Singapore:  World Scientific.  (Collection of reprints.)

E.N. Lorenz, 1963.  Deterministic Non-Periodic Flow.  J. Atmosph. Sci.  20, 130-141.

B.B. Mandelbrot, 1983.  The Fractal Geometry of Nature.  New York:  W.H. Freeman.

R. Mañe, 1987.  Ergodic Theory and Differentiable Dynamics.  New York, Berlin, Heidelberg, and Tokyo:  Springer-Verlag.

R.M. May, 1976.  Simple Mathematical Models with Very Complicated Dynamics.  Nature  261, 456-467.

J.L. MCCauley, 1988.  An Introduction to Nonlinear Dynamics and Chaos Theory. Physica Scripta T20.  (Available from The Royal Swedish Academy of Sciences, Physica Scripta, Box 50005, S-104 05 Stockholm, Sweden, for $25.00 in check or Visa,MC,AMEX cards.)

J.D. Meiss, 1992.  Symplectic maps, variational principles, and transport.  Rev. Mod. Phys. 64, 795-848.

F.C. Moon, 1987.  Chaotic Vibrations, An Introduction for Applied Scientists and Engineers.  New York:  J. Wiley.

V.V. Nemytskii and V.V. Stepanov, 1960.  Qualitative Theory of Differential Equations.  Princeton:  Princeton University Press.  

D.S. Ornstein and B. Weiss, 1991.  Statistical Properties of Chaotic Systems, Bull. Amer. Math. Soc 24(1991)11-116.

T.S. Parker and L.O. Chua, 1987.  Chaos:  A Tutorial for Engineers.  Proc. IEEE  75(1987)982-1008.

V. Poénaru, 1979.  An Informal Crash Course on Ergodic Theory (from a Topologist's Standpoint), in:  La Matière Mal Consensé/Ill-Condensed Matter, R. Balian, R. Maynard, and G. Toulouse, eds.  Amsterdam, New York, and Oxford:  North-Holland.

H. Poincaré,  1892.  Les Méthodes Nouvelles de la Mécanique Céleste.  Paris:  Gauthier-Villars.

S.N. Rasband, 1989.  Chaotic Dynamics of Nonlinear Systems.  New York:  John Wiley.

W. Rudin, 1966.  Real and Complex Analysis.  New York:  McGraw-Hill.

D. Ruelle, 1989a.  Elements of Differentiable Dynamics and Bifurcation Theory.  Boston:  Academic Press.

D. Ruelle, 1989b.  Chaotic Evolution and Strange Attractors. Cambridge:  Cambridge University Press.

C.E. Shannon and W. Weaver, 1949.  The Mathematical Theory of Communication.  Urbana, Illinois:  University of Illinois Press. 

A.N. Ùarkovskii£, 1964.  Sosu≤estvovanie ciklov nepreryvnogo preobrazovaniq prqmoi£ v sebq.  Ukr. mat. Ωurnal 16, 61-71.  (A.N. Sharkovskii, Co-existence of the cycles of a continuous mapping of the line into itself, Ukr. Math. Journal  16,61-71)

G.F. Simmons, 1972.  Differential Equations, with Applications and Historical Notes.  New York:  McGraw-Hill.  

Ya.G. Sinai, 1976.  Introduction to Ergodic Theory, translated by V SCHEFFER.  Princeton:  Princeton University Press.

S. Smale, 1967.  Diferentiable Dynamical Systems. Bull. Amer. Math. Soc.  73, 747-817.

S. Smale, 1980.  The Mathematics of Time:  Essays on Dynamical Systems, Economic Processes, and Related Topics.  New York, Berlin, Heidelberg, and Tokyo:  Springer-Verlag.

W. Thirring, 1978.  Classical Dynamical Systems, translated by E.M. HARRELL.  New York and Vienna: Springer-Verlag.

W. Thirring, 1980.  Quantum Mechanics of Large Systems, translated by E.M. HARRELL.  New York and Vienna: Springer-Verlag.

C.J. Thompson, 1972.  Mathematical Statistical Mechanics.  Princeton:  Princton University Press.

S. Wiggins, 1988.  Global Bifurcations and Chaos: Analytical Methods.  New York, Berlin, Heidelberg, and Tokyo:  Springer-Verlag.

S. Wiggins, 1990.  Introduction to Applied Nonlinera Dynamical Systems and Chaos, Texts in Applied Mathematics 2.  New York, Berlin, Heidelberg, London, Paris, Tokyo, and Hong Kong:  Springer-Verlag.

J. Wisdom, 1987.  Urey Prize Lecture:  Chaotic Dynamics in the Solar System.  Icarus  72, 241-275.

K Yosida, 1980.  Functional Analysis.  New York, Berlin, Heidelberg, and Tokyo:  Springer-Verlag.

L.S. Young, 1983.  Entropy, Lyapunov Exponents, and Hausdorff Dimension in Differentiable Dynamical Systems, IEEE Trans. Circ. Syst. 30(1983)599-XXX.

SOFTWARE

Chaos, by B. Wahl, 1989, published by Dynamic Software, P.O. Box 7534, Santa Cruz  CA  95061.  (Macintosh)

Dynamical Systems, by H. Gollwitzer, 1991, published by U’Betcha Publications, 554 Evans Rd., Springfield  PA  19064.  (Macintosh)

Mathematica, by Wolfram Research, Inc., P.O. Box 6059, Champaign  IL  61826-6059.  (Compatible with various machines.)

Phaser, by H. Koçak, 1990, published by Springer-Verlag, New York with the book Differential and Difference Equations through Computer Experiments.  (MS-DOS machines)