References List, ME 960.
Characterization of Nonlinear
Systems
Books
- R.H. Abraham and C. D. Shaw, 1992, Dynamics: The Geometry of
Behavior, Addison-Wesley, Redwood City. (on reserve*--this book
has an excellent graphical perspective on the geometry of the
phase space, attractors, chaos, etc.)
- H. Abarbanel, M. Gilpin, and M. Rotenberg, 1996, Analysis of
Observed Chaotic Data, Springer, NY (on reserve*--this book covers
several of our topics).
- G. L. Baker and J. P. Gollub, 1996, Chaotic Dynamics: An
Introduction, Cambridge University Press, NY (on reserve*).
- H. Peitgen, H. Jigens, D. Saupe, 1992, Chaos and Fractals: New
Frontiers in Science, Springer, NY (on reserve*).
- E. Ott, 1993, Chaos in Dynamical Systems, Cambridge University
Press, NY (on reserve*).
- F. C. Moon, 1992, Chaotic and Fractal Dynamics, Wiley, NY (on
reserve*).
- A. Weigend and N. Gershenfeld, eds., 1992, Time Series
Prediction, Addison-Wesley, Reading MA (on reserve*)
- H. Krantz and T. Schreiber, 1997, Nonlinear Time Series
Analysis, Cambridge University Press, NY (on reserve*)
- N. Tufillaro, T. Abbott, and J. Reilly, 1992, An Experimental
Approach to Nonlinear Dynamics and Chaos, Addison Wesley, Redwood
City. (on reserve*--this book is good on the unstable periodic
orbits--knots and templates)
- J. A. Yorke, Chaos: An Introduction to Dynamical Systems.
- G. P. Williams, Chaos Theory Tamed.
- Jens Feder, 1988, Fractals.
- B. Mandelbrot, 1983, The Fractal Geometry of Nature, W. H.
Freeman and Co., New York.
- M. Barnsley, 1988, Fractals Everywhere, Academic Press,
Boston.
- P. Bak, 1996, How Nature Works: The Science of Self-Organized
Criticality, Springer-Verlag, New York.
* Reserved books are at the Engineering Library
Papers
- G. Berkooz, P. Holmes, and J. L. Lumley, 1993, "The proper
orthogonal decomposition in the analysis of turbulent flows,"
Annual Review of Fluid Mechanics, 25, 539-575.
- Broomhead and King, 1986, "Extracting Qualitative Dynamics
from Experimental Data," Physica D, 20, 217-236.
- J. P. Cusumano, M. T. Sharkady, B. W. Kimble, 1993, "Spatial
coherence measurements of a choatic flexible beam impact
oscillator," in Aerospace Structures: Nonlinear Dynamics and
System Response, J. P. Cusumano, C. Pierre, and S. T. Wu (eds.),
ASME AD-Vol. 33, 13-22.
- B. F. Feeny, 1997, "Interpreting POMs in vibrations," DETC-97,
Sacramento, on CD-ROM. (preprint)
- B. F. Feeny, 2000, "Fast multifractal analysis by recursive
box covering," International Journal of Bifurcation and Chaos,
expected volume 10, number 9. (preprint,
figures)
- B. F. Feeny and R. Kappagantu, 1998, "On the physical
interpretation of proper orthogonal modes in vibrations," Journal
of Sound and Vibration 211 (4) 607-616.
(preprint)
- B. F. Feeny and J. W. Liang, 1997, "Phase-space
reconstructions and stick-slip," Nonlinear Dynamics 13 (1), 39-57.
(preprint)
- N. Gershenfeld, 1988, "An experimentalist's introduction to
the observation of dynamical systems," in Directions in Chaos, II,
Hao Bai Lin, ed., 310-384.
- H. Gould and J. Tobochnik, 1990, More on fractals and chaos:
multifractals, Computers in Physics, Mar/Apr, 202-207.
- P. Grassberger, 1983, Generalized dimensions of strange
attractors, Physics Letters A 97 (6) 227-230.
- P. Grassberger and I. Procaccia, 1983, Characterization of
strange attractors, Physical Review Letters 50 (5) 346-349.
- T. C. Halsey et al., 1986, Fractal measures and their
singularities: the characterization of strange sets, Physical
Review A 33 (2) 1141-1151.
- H. Hentschel and I. Procaccia, 1983, The infinite number of
generalized dimensions of fractals and strange attractors, Physica
D 8, 435-444.
- M. H. Jensen et al., 1985, Global universality at the onset of
chaos: results of a forced Rayleigh-Benard experiment, Physical
Review Letters 55 (25) 2798-2801.
- Kennel, Brown and Abarbanel, 1992, "Determining embedding
dimension for phase-space reconstruction using a geometrical
construction," Physical Review A, 45, 3403-3411.
- F. A. McRobie and J. M. T. Thompson, 1993, "Braids and Knots
in Driven Oscillators," Int. J. Bifurcation and Chaos 3 (6)
1343-1362.
- F. A. McRobie and J. M. T. Thompson, 1994, "Knot types and and
bifurcation sequences of homoclinic and transient orbits of a
single-degree-of-freedom driven oscillator," Dynamics and
Stability of Systems 9 (3) 223-252.
- L. Noakes, 1991, "The Takens embedding theorem," International
Journal of Bifurcation and Chaos, 1 (4) 867-872.
- V. I. Oseledec, 1968, "A multiplicative ergodic theorem.
Ljapunov characteristic numbers for dynamical systems,"
Transactions of the Moscow Mathematical Society 19, 197-231.
- K. Pawelzik and H. G. Schuster, 1987, "Generalized dimensions
and entropies from a measured time series," Physical Review A 35
(1) 481-484.
- F. Takens, 1981, "Detecting strange attractors in turbulence,"
in Dynamical Systems and Turbulence, Warwick 1980, D.A. Rand and
L. S. Young, eds., Lecture Notes in Mathematics, Vol. 898,
Springer, 366-381.
- J. Theiler, 1990, "Estimating fractal dimension," Journal of
the Optical Society of America A 7 (6) 1055-1073.
- H. Ueda, 1995, "Usefulness of multifractal analysis for galaxy
distributions," Publ. Astron. Soc. Japan (PASJ) 47, 389-395.
