Nicholas B. Tufillaro, Tyler Abbott, Jeremiah Reilly, An Experimental Approach
to Nonlinear Dynamics and Chaos, Addison-Wesley Publishing Company, 1992.
ISBN 0-201-55441-0.
(Good undergraduate introduction with an emphasis on specific physical examples and
experimental techniques. Updates to the Macintosh programs include in the text are
available by electronic transfer from the first author---nbt@reed.edu.)
R. Devaney, An introduction to Chaotic Dynamical Systems, (Addison-Wesley, Reading, MA, 1989).
Andreas S. Weigend and Neil A. Gershenfeld (editors), Time Series Prediction: Forecasting the future and understanding the past, Proceedings of he NATO Advanced Research Workshop on Comparative Time Series Analysis held in Santa Fe, New Mexico, May 14-17, 1992, Proceedings Volume XV, Santa Fe Institute Studies in the Sciences of Complexity, Addison-Wesley Publishing Company, 1994.
Welington de Melo and Sebastina van Strien, One-Dimensional Dynamics, Springer-Verlag (1993).
L. Block and W. A. Coppel, Dynamics in one dimension, Lecture Notes in Math. 1513, Springer, 1992.
D. Schlomiuk (editor), Bifurcations and Periodic Orbits of Vector Fields, Proceedings of the NATO Advanced Study Institute and Seminaire de Mathematiques superieures on Bifurcations and Periodic orbits of Vector Fields, Montreal, Canada, July 13-24, 1992, Kluwer Academic Publishers, 1993.
P. Boyland and T. Hall, Dynamics of Surface Homeomorphisms, World Scientific (to appear).
Mark Pollicot, Lectures on ergodic theory and Pesin theory on compact manifolds, London Mathematical Society Lecture Notes 180, Cambridge University Press, 1993.
Robert Gilmore, Castrophe Theory for Scientists and Engineers, Dover Publications Inc, 1981.
David Ruelle, Chance and Chaos, Penguin, 1993. (in my humble opinion the best introduction to what "complexity theory" may be all about).
J. Hale and H. Kocak, Dynamics and Bifurcations, Springer-Verlag, Texts in Applied Mathematics 3, 1991.
Jack K. Hale, Oscillations in Nonlinear Systems, Dover Publications Inc, 1963.
Ya. S. Sinai, Topics in Ergodic Theory, Princton University Press, Princeton, NJ, 1994.
Jerold E. Marsden, Lectures on Mechanics, London Mathematical Society Lecture Note Series 174, Cambridge University Press, 1992.
V. I. Arnold, Topological Invariants of Plane Curves and Caustics, University Lecture Series, Volume 5, American Mathematical Society, 1991.
Physical Review Letters (American Physical Society)
Physics Letters (North-Holland)
Europhysics Letters
Physica D (North-Holland)
Physical Review E (American Physical Society)
Chaos (American Institute of Physics)
Nonlinearity (non@iopublishing.co.uk)
Journal of Nonlinear Science & Nonlinear Science Today (Springer-Verlag)
International Journal of Bifurcations and Chaos (World Scientific)
Nonlinear Dynamics (Kluwer Academic)
Dynamics & Stability of Systems (Carfax Pub. Co.)
Ergodic Theory and Dynamical Systems (Cambridge University Press)
Journal of Statistical Physics
Journal of Physics A and E
Journal of Sound and Vibration
Journal de Physique
Journal de Physique Letters
Journal of the Acoustical Society of America
Journal of the Optical Society of America B
Communications in Mathematical Physics
Journal of Fluid Mechanics
Proc. of the Royal Society
Physica Scripta
Journal of the Chemical Physics
Journal of Mathematical Physics
Bull. Am. Math. Soc.
Quaterly of Applied Math
J. of Rational Mechanics and Analysis
American Journal of Physics
Physics World (http://www.iop.org, pwld@iopublishing.co.uk)
Reviews of Modern Physics
Physics Reports
Computers and Physics
The Physics Teacher
European Journal of Physics
Physics World
Contemporary Physics
American Mathematical Monthly
Mathematical Intelligencer
Physics Today
Nonlinear Science Today
Info World
Byte
MacWorld
Science News
The Scientist
Electronics
Chronicle of Higher Education
Nature
P. G. Drazin and G. P. King (editors), Interpretation of Time Series from Nonlinear Systems, Proceedings of the IUTAM Symposium and NATO Advanced Research Workshop on the Interpretation of Time Series from Nonlinear Mechanical Systems, University of Warwick, England, 26-30 August 1991, Physica D 58 (1-4), 15 September 1992.
H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, Reviews of Modern Physics 65, 1331 (1993).
R. Badii et. al., Progess in the analysis of experimental chaos through periodic orbits, Reviews of Modern Physics, 66 (4), 1389-1415 (October 1994).
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J. Milnor and W. Thurston, in Dynamical Systems, edited by J. Alexander, Lecture Notes in Math. Vol. 1342 (Springer-Verlag, Berlin, 1988), p. 465.
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T. Hall, Nonlinearity 7, 367 (1994); ibid 7, 861 (1994).
G. B. Mindlin, H. Solari, M. Natiello, R. Gilmore, and X-J. Hou, J. Nonlinear Sci. 1, 146 (1991).
G. B. Mindlin and R. Gilmore, Physica D 58, 229 (1992).
G. B. Mindlin, X-J. Hou, H. G. Solari, R. Gilmore, and N. B. Tufillaro, Phys. Rev. Lett. 64, 2350 (1990).
F. Papoff, E. Arimondo, F. Fioretto, G. B. Mindlin, H. G. Solari, and R. Gilmore, Phys. Rev. Lett. 68, 1128 (1992).
G. B. Mindlin, R. Lopez-Ruiz, H. G. Solari, and R. Gilmore, Phys. Rev. E 46, 4297 (1993).
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M. Lefranc, P. Glorieux, F. Papoff, F. Molesti, and E. Arimondo, Combining Topological Analysis and Symbolic Dynamics to Describe a Strange Attractor and Its Crises, Physical Review Letters 73 (10), 1364-1367 (Sept. 1994).
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T. Matsuoka, in Dynamical systems and nonlinear oscillations, edited by G. Ikegami (World Scientific, Singapore, 1986) p. 58; Invent. Math. 70, 319 (1983); J. Diff. Eqs. 76, 190 (1988).
P. Melvin and N. B. Tufillaro, Phys. Rev. A bf 44, R3419 (1991).
P. Cvitanovic, G. H. Gunaratne, and I. Procaccia, Phys. Rev. A 38, 1503 (1988); K. T. Hansen, Symbolic dynamics in chaotic systems, Ph.D. Thesis, Univ. of Oslo (1993).
N. B. Tufillaro, Braid analysis of (low-dimensional) chaos (e-print, 1993).
A. Sarkovskii, Ukrain. Mat. Z. 16 (1964), 61.
S. Baldwin, Discrete Math. 67, 111 (1987); C. Bernhardt, E. Coven, M. Misiurewicz, and I. Mulvey, Trans. Am. Math. Soc. 333, 701 (1992).
M. Bestvina and M. Handel, Ann. Math. 135, 1 (1992); ``Train tracks for surface homeomorphisms,'' (1992, unpublished).
J. Los, ``Pseudo-Anosov maps and invariant train tracks in the disc: a finite algorithm,'' Proc. Lond. Math. Soc. 66, 400 (1993).
J. Franks and M. Misiurewicz, ``Cycles for disk homeomorphisms and thick trees,'' in Contemporary Mathematics 152, C. K. McKord, ed. (AMS, Prov. RI, 1993)
D. Auerbach, P. Cvitanovic, J.-P. Eckmann, G. Gunaratne, and I. Procaccia, Phys. Rev. Lett. 58 2387 (1987).
N. B. Tufillaro, H. Solari, and R. Gilmore, Phys. Rev. A 41, 5717 (1990).
P. Cvitanovic and B. Eckhardt, Nonlinearity 6, 277 (1993), and references therein.
T. Li and J. Yorke, Amer. Math. Monthly 82, 985 (1975).
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P. Grassberger, H. Kantz, and U. Moenig, J. Phys. A 22, 5217 (1989).
N. B. Tufillaro, P. Wyckoff, R. Brown, T. Schreiber, and T. Molteno, Topological time series analysis of a string experiment and its synchronized model, Physical Review E 51 (1), 164-174 January 1995.
N. B. Tufillaro, Braids of a bouncing ball, Physical Review E 50 (6), 4509-4522 December 1994.
R. Brown, N. Rulkov, and N. B. Tufillaro, The effects of additive noise and drift in the dynamics of the driving on chaotic synchronization, Physics Letters 162A, 201-205 (1994).
R. Brown, N. Rulkov, and N. B. Tufillaro, Synchronization of chaotic systems: the effects of additive noise and drift in the dynamics and driving, Physical Review E 50 (6), 4488-4508 December 1994.
N. B. Tufillaro, Topological organization of (low-dimensional) chaos, in NATO-ASI proceedings, From statistical physics to statistical inference and back, J.-P. Nadal and P. Grassberger editors, Kluwer Academic Publishers (1994).
N. B. Tufillaro, R. Holzner, L. Flepp, E. Brun, M. Finardi, and R. Badii, Template analysis for a chaotic NMR-laser, Physical Review A 44 (8), R4786 (1991).
P. Melvin and N. B. Tufillaro, Templates and framed braids, Physical Review A 44 (6), R3416 (1991).
G. B. Mindlin, X-J Hou, H. G. Solari, R. Gilmore, and N. B. Tufillaro, Classification of strange attractors by integers, Physical Review Letters 64 (20), 2350 (1990).
N. B. Tufillaro, H. G. Solari, and R. Gilmore, Relative rotation rates: fingerprints for strange attractors, Physical Review A 41 (10), 5717 (1990).
R. Gilmore and J. W. L. McCallum, Structure in the bifurcation diagram of the Duffing oscillator, Physical Review E 51 (2), 935-956 (1995).
Gabriel B. Mindlin and Ricardo Lopez-Ruiz, Hernan G. Solari, and R. Gilmore, Horseshoe implications, Physical Review E 48 (6), 4297-4304 December 1993.