String References in BibTex from
Tim Molteno's Ph.D Thesis
Chaos and Crisis in Strings
Otago University, Dunedin, New Zealand
1994.
--------------------------------------------------------------------------
@string{PLA = "Physics Letters A"}
@string{PRL = "Physical Review Letters"}
@string{PRA = "Physical Review A"}
@string{PRE = "Physical Review E"}
@string{JSV = "Journal of Sound and Vibration"}
%********************************* INTRODUCTION ***************
@BOOK{Tufillaro92,
AUTHOR = "Tufillaro, N.B. and Abbot, T. and Reilly, J.",
TITLE = "An experimental approach to nonlinear dynamics and chaos",
SERIES = "Addison-Wesley studies in nonlinearity",
PUBLISHER = "Addison-Wesley",
YEAR = 1992}
@BOOK{Abraham88v4,
AUTHOR = "Abraham, R. H. and Shaw, C. D.",
TITLE = "Dynamics: the Geometry of Behaviour",
VOLUME = 4,
PUBLISHER = "Aeriel Press",
YEAR = 1988}
@article{Harrison48,
AUTHOR = "Harrison, H.",
TITLE = "Plane and circular motion of a string",
JOURNAL = "J. Acoust. Soc. Am.",
VOLUME = 20,
NUMBER = 6,
YEAR = 1948,
PAGES = {874}}
@article{Oplinger60,
AUTHOR = "Oplinger, D.",
TITLE = "Frequency response of a nonlinear stretched string",
JOURNAL = "J. Acoust. Soc. Am.",
VOLUME = 32,
NUMBER = 12,
YEAR = 1960}
@article{Murthy65,
AUTHOR = "Murthy, G. and Ramakrishna, B.",
TITLE = "Nonlinear character of resonance in stretched strings",
JOURNAL = "J. Acoust. Soc. Am.",
VOLUME = 38,
NUMBER = 4,
YEAR = 1965}
@article{Tufillaro91,
AUTHOR = "Tufillaro, N.B and Holzner, R. and Flepp, L. and Brun, E. and Finardi, M. and Badii, R.",
TITLE = "Template analysis for a chaotic NMR laser",
JOURNAL = PRA,
VOLUME = 44,
NUMBER = 8,
YEAR = 1991,
PAGES = {4786-4788}}
@article{Flepp91,
AUTHOR = "Flepp, L. and Holzner, R. and Brun, E.",
TITLE = "Model identification by Periodic-Orbit analysis for NMR-Laser Chaos",
JOURNAL = PRL,
VOLUME = 67,
NUMBER = 17,
YEAR = 1991,
PAGES = {2244-2247}}
@article{Lorenz63,
AUTHOR = "Lorenz, E.N.",
TITLE = "Deterministic Nonperiodic Flow",
JOURNAL = "J. Atmos. Sci.",
VOLUME = 20,
YEAR = 1963,
PAGES = {130}}
@article{Gollub75,
AUTHOR = "Gollub, J.P. and Swinney, H.L.",
TITLE = "Onset of turbulence in a rotating fluid",
JOURNAL = PRL,
VOLUME = 35,
YEAR = 1975,
PAGES = {927}}
@article{Swinney78,
AUTHOR = "Swinney, H.L. and Gollub, J.P.",
TITLE = "Transition to turbulence",
JOURNAL = "Physics Today",
VOLUME = 31,
NUMBER = 8,
MONTH = "August",
YEAR = 1978,
PAGES = {41}}
@article{Moon79,
AUTHOR = "Moon, F.C. and Holmes, P.J.",
TITLE = "A magnetoelastic strange attractor",
JOURNAL = JSV,
VOLUME = 65,
YEAR = 1979,
PAGES = {285}}
%********************************* CHAPTER 2 ***************
@article{Molteno90,
AUTHOR = "Molteno, T.C.A. and Tufillaro, N.B.",
TITLE = "Torus Doubling and Chaotic String Vibrations: Experimental results",
JOURNAL = JSV,
VOLUME = 137,
NUMBER = 2,
YEAR = 1990,
PAGES = {327-330}}
@article{Johnson89,
AUTHOR = "Johnson, J.M. and Bajaj, A.K.",
TITLE = "Amplitude modulated and chaotic dynamics in resonant motion
of strings",
JOURNAL = JSV,
VOLUME = 128,
NUMBER = 1,
YEAR = 1989,
PAGES = {87-107}}
@article{Bajaj92,
AUTHOR = "Bajaj, A.K. and Johnson, J.M.",
TITLE = "On the amplitude dynamics and crisis in resonant motion of
stretched strings",
JOURNAL = "Phil. Trans. R. Soc. London A",
VOLUME = 338,
YEAR = 1992,
PAGES = {1-41}}
@article{Miles84,
AUTHOR = "Miles, John.",
TITLE = "Resonant, nonplanar motion of a stretched string",
JOURNAL = "J. Acoust. Soc. Am.",
VOLUME = 75,
NUMBER = 5,
YEAR = 1984,
PAGES = {1505-1010}}
@article{Miles93,
AUTHOR = "Miles, John.",
TITLE = "Damped Spherical Pendulum",
JOURNAL = JSV,
VOLUME = 140,
NUMBER = 5,
YEAR = 1993,
PAGES = {327-330}}
@article{Knobloch83,
AUTHOR = "Knobloch, E. and Weiss, N.O.",
TITLE = "Bifurcations in a model of magnetoconvection",
JOURNAL = "Physica D",
VOLUME = 9,
YEAR = 1983,
PAGES = {379-407}}
@article{Tufillaro93,
AUTHOR = "Tufillaro, N.B.",
TITLE = "Braid analysis of (low-dimensional) chaos",
JOURNAL = PRE,
YEAR = 1994,
PAGES = {to appear}}
@article{Halsey86,
AUTHOR = "Halsey, T.C. and Jensen, M.H. and Kadanoff, L.P. and Procaccia, I. and Shraiman, B.I.",
TITLE = "Fractal measures and their singularities: The characterization of strange sets",
JOURNAL = PRA,
VOLUME = 33,
NUMBER = 2,
YEAR = 1986,
PAGES = {1141-1151}}
@article{Farmer83,
AUTHOR = "Farmer, J.D. and Ott, E. and Yorke, J.A.",
TITLE = "The dimension of chaotic attractors",
JOURNAL = "Physica D",
VOLUME = 7,
YEAR = 1983,
PAGES = {153-180}}
@article{Hou90,
AUTHOR = "Hou,X--.J. and Gilmore,R. and Mindlin,G.B. and Solari,H.G.",
TITLE = "An efficient algorithm for fast $O(N*\ln(N))$ box counting",
JOURNAL = PLA,
VOLUME = 151,
NUMBER = {1,2},
YEAR = 1990,
PAGES = 43}
@article{Liebovitch89,
AUTHOR = "Liebovitch,L.S. and Toth, T.",
TITLE = "A fast algorithm to determine fractal dimensions by box counting",
JOURNAL = PLA,
VOLUME = 141,
NUMBER = {8,9},
YEAR = 1989,
PAGES = 386}
@article{Block90,
AUTHOR = "Block, A. and von Bloh,W. and Schnellnhuber,H.J.",
TITLE = "Efficient box-counting determination of generalized fractal dimensions",
JOURNAL = PRA,
VOLUME = 42,
NUMBER = 4,
YEAR = 1990,
PAGES = 1869}
@article{Meisel92,
AUTHOR = "Meisel L.V. and Johnson,M. and Cote, P.J.",
TITLE = "Box-counting multifractal analysis",
JOURNAL = PRA,
VOLUME = 45,
NUMBER = 10,
YEAR = 1992,
PAGES = {6989,6996}}
@article{Ling92,
AUTHOR = "Ling, F.H. and Schmidt, G.",
TITLE = "Box-Counting and Dimensional Analysis of a Pulsar",
JOURNAL = "Journal of Computational Physics",
VOLUME = 99,
YEAR = 1992,
PAGES = 196}
@article{Grassberger83A,
AUTHOR = "Grassberger, P.",
TITLE = "on the fractal dimension of the Henon attractor",
JOURNAL = PLA,
VOLUME = 97,
NUMBER = 6,
YEAR = 1983,
PAGES = {224-226}}
@article{Grassberger83B,
AUTHOR = "Grassberger, P.",
TITLE = "Generalized dimensions of strange attractors",
JOURNAL = PLA,
VOLUME = 97,
NUMBER = 6,
YEAR = 1983,
PAGES = {227-230}}
@article{Grassberger87,
AUTHOR = "Grassberger, P. and Procaccia, I.",
TITLE = "FIND THIS TITLE",
JOURNAL = PRL,
VOLUME = 58,
YEAR = 1987,
PAGES = {2387-2389}}
@article{Grassberger90,
AUTHOR = "Grassberger,P.",
TITLE = "An optimized box-assisted algorithm for fractal dimensions",
JOURNAL = PLA,
VOLUME = 148,
NUMBER = {1,2},
YEAR = 1990,
PAGES = {63-68}}
@article{Theiler90,
AUTHOR = "Theiler,J.",
TITLE = "Estimating fractal dimension",
JOURNAL = "J. Optical Soc. America A",
VOLUME = 7,
NUMBER = 6,
YEAR = 1990,
PAGES = {1055-1073}}
@article{Eckmann92,
AUTHOR = "Eckmann,J.--P. and Ruelle, D.",
TITLE = "Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems",
JOURNAL = "Physica D",
VOLUME = 56,
YEAR = 1992,
PAGES = {185-187}}
@article{Greenside82,
AUTHOR = "Greenside,H.S. and Wolf,A. and Swift,J. and Pignataro,T.",
TITLE = "Impracticality of a box-counting algorithm for calculating the dimensionality of strange attractors",
JOURNAL = PRA,
VOLUME = 25,
NUMBER = 6,
YEAR = 1982,
PAGES = 3543}
!*********************************************************************
@BOOK{Ruelle89,
AUTHOR = "Ruelle,David",
TITLE = "Chaotic Evolution and Strange Attractors",
PUBLISHER = "Cambridge",
YEAR = 1989}
@BOOK{Morse68,
AUTHOR = "Morse, P.M. and Ingard, K.U.",
TITLE = "Theoretical Acoustics",
PUBLISHER = "McGraw-Hill",
YEAR = 1968}
@BOOK{Morse36,
AUTHOR = "Morse, P.M.",
TITLE = "Vibration and Sound",
EDITION = "second",
PUBLISHER = "McGraw-Hill",
YEAR = 1936}
@BOOK{Arnold83,
AUTHOR = "Arnold,V.I.",
TITLE = "Geometrical methods in the theory of ordinary differential equations",
PUBLISHER = "Springer-Verlag",
YEAR = 1983}
!*********************************************************************
! Periodic orbit Extraction References
@article{Auerbach87,
AUTHOR = "Auerbach, D. and Cvitanovic, P. and Eckmann, J.-P. and Gunaratne, G. and Procaccia, I.",
TITLE = "Exploring chaotic motion through periodic orbits",
JOURNAL = PRL,
VOLUME = 58,
NUMBER = 23,
YEAR = 1987,
PAGES = 2387}
@article{Bowen70,
AUTHOR = "Bowen, R.",
TITLE = "Markov Partitions for Axiom A diffeomorphisms",
JOURNAL = "American Journal of Mathematics",
VOLUME = 92,
YEAR = 1970,
PAGES = 725}
@BOOK{Bowen78,
AUTHOR = "Bowen, R.",
TITLE = "On Axiom A diffeomorphisms",
SERIES = "CBMS Regional conference series in mathematics",
VOLUME = 35,
PUBLISHER = "A M S Publications",
ADDRESS = "Providence",
YEAR = 1970}
@BOOK{Crowell63,
AUTHOR = "Crowell, R.H. and Fox, R.H.",
TITLE = "Introduction to Knot Theory",
PUBLISHER = "Ginn and Co",
ADDRESS = "Boston",
YEAR = 1963}
@article{Cvitanovic88,
AUTHOR = "Cvitanovic, P.",
TITLE = "Invariant measures of strange sets in terms of cycles",
JOURNAL = PRL,
VOLUME = 61,
NUMBER = 24,
YEAR = 1988,
PAGES = 2729}
@article{Eckmann85,
AUTHOR = "Eckmann, J.-P. and Ruelle, D.",
TITLE = "Ergodic theory of chaos and strange attractors",
JOURNAL = "Rev. Mod. Phys",
VOLUME = 57,
NUMBER = 3,
YEAR = 1985,
PAGES = 617}
@article{Lathrop89,
AUTHOR = "Lathrop, D.P. and Kostelich, E.J.",
TITLE = "Characterization of an experimental
Strange Attractor by periodic orbits",
JOURNAL = PRA,
VOLUME = 40,
NUMBER = 7,
YEAR = 1989,
PAGES = {4028-4031}}
@BOOK{Guckenheimer83,
AUTHOR = "Guckenheimer, J. and Holmes, P.",
TITLE = "Nonlinear Oscillations, Dynamical Systems,
and Bifurcations of Vector Fields",
PUBLISHER = "Springer-Verlag",
ADDRESS = "New York",
YEAR = 1983}
@article{Mindlin90,
AUTHOR = "Mindlin, G.B. and Hou, X.-J. and Solari, H.G. and Gilmore, R. and Tufillaro, N.B.",
TITLE = "Classification of Strange attractors by integers",
JOURNAL = PRL,
VOLUME = 64,
NUMBER = 20,
YEAR = 1990,
PAGES = {2350-2354}}
@BOOK{Poincare1892,
AUTHOR = "Poincar\'e, H.",
TITLE = "Les Methodes Nouvelles de la Mechanique Celeste",
VOLUME = 1,
PUBLISHER = "Gauthier-Vallars",
ADDRESS = "Paris",
YEAR = 1892}
@BOOK{Press86,
AUTHOR = "Press, W.H. and Flannery, B.P. and Teukolsky, S.A. and Vetterling, W.T.",
TITLE = "Numerical Recipes: the art of scientific computing",
PUBLISHER = "Cambridge University Press",
ADDRESS = "Cambridge",
YEAR = 1986}
@article{Solari88,
AUTHOR = "Solari, H.G. and Gilmore, R.",
TITLE = "Relative Rotation Rates for driven Dynamical Systems",
JOURNAL = PRA,
VOLUME = 37,
NUMBER = 8,
YEAR = 1988,
PAGES = 3096}
@article{Sparrow83,
AUTHOR = "Sparrow, C.",
TITLE = "An introduction to the Lorenz Equations",
JOURNAL = "IEEE CAS",
VOLUME = 30,
NUMBER = 8,
YEAR = 1983,
PAGES = {533,541}}
@phdthesis{TufillaroPHD,
AUTHOR = "Tufillaro, N.B.",
TITLE = "Chaotic themes from strings",
SCHOOL = "Bryn Mawr College",
MONTH = "April",
YEAR = 1990}
!******************
@BOOK{Moon87,
AUTHOR = "Moon, F.C.",
TITLE = "Chaotic Vibrations: an introduction for applied scientists and engineers",
PUBLISHER = "John Wiley \& sons",
ADDRESS = "New York",
YEAR = 1987}
@article{Tufillaro89,
AUTHOR = "Tufillaro, N.B.",
TITLE = "Nonlinear and chaotic string vibrations",
JOURNAL = "American Journal of Physics",
VOLUME = 30,
NUMBER = 8,
YEAR = 1989}
@article{Kaneko84,
AUTHOR = "Kaneko, K.",
TITLE = "Oscillation and doubling torus",
JOURNAL = "Progress of Theoretical Physics",
VOLUME = 72,
YEAR = 1984,
PAGES = {202-215}}
@article{Arneodo83,
AUTHOR = "Arneodo, A. and Coullet, P.H. and Spiegel, E.A.",
TITLE = "Cascade of period doubling tori",
JOURNAL = PLA,
VOLUME = 94,
YEAR = 1983,
PAGES = {1-5}}
@article{Gough84,
AUTHOR = "Gough, C.",
TITLE = "The nonlinear free vibration of a damped elastic string",
JOURNAL = "J. Acoustical Soc. Am.",
VOLUME = 75,
YEAR = 1984,
PAGES = {1770-1776}}
@article{Hanson87,
AUTHOR = "Hanson, R.",
TITLE = "Optoelectronic detection of string vibration",
JOURNAL = "The Physics Teacher",
MONTH = "March",
YEAR = 1987,
PAGES = {165-166}}
@article{Grassberger83C,
AUTHOR = "Grassberger, P. Procaccia, I.",
TITLE = "Measuring the Strangeness of Strange Attractors",
JOURNAL = "Physica D",
VOLUME = 9,
YEAR = 1983,
PAGES = {189-208}}
@article{Coullet88,
AUTHOR = "Coullet, P. and Lega, J.",
TITLE = "Defect-mediated turbulence in wave patterns",
JOURNAL = "Europhysics Letters",
VOLUME = 7,
NUMBER = 6,
YEAR = 1988,
PAGES = {511-516}}
% *********************************************************
% ******* references for the StringII setup chapter *******
@article{Narasimha68,
AUTHOR = "Narasimha, R.",
TITLE = "Non-linear vibration of an elastic string",
JOURNAL = JSV,
VOLUME = 8,
NUMBER = 1,
YEAR = 1968,
PAGES = {134-146}}
@article{OReilly92,
AUTHOR = "O'Reilly, O. and Holmes, P.J.",
TITLE = "Non-linear, non-planar and non-periodic vibrations of a string",
JOURNAL = JSV,
VOLUME = 153,
NUMBER = 3,
YEAR = 1992,
PAGES = {413-435}}
@article{Ott90,
AUTHOR = "Ott, E. and Gregobi, C. and Yorke, J.A.",
TITLE = "Controlling Chaos",
JOURNAL = PRL,
VOLUME = 64,
NUMBER = 11,
YEAR = 1990,
PAGES = {1196-1199}}
@article{Parker87,
AUTHOR = "Parker, T.S. and Chua, L.O.",
TITLE = "Chaos: a tutorial for engineers",
JOURNAL = "Proceedings of the IEEE",
VOLUME = 75,
NUMBER = 8,
YEAR = 1987,
PAGES = {982-1008}}
@BOOK{Feather64,
AUTHOR = "Feather, N.",
TITLE = "Vibrations and waves",
PUBLISHER = "Penguin",
ADDRESS = "Middlesex",
YEAR = 1964}
@BOOK{DDSArticle,
AUTHOR = "Chrysafis, A.",
TITLE = "Digital sine-wave synthesis using the DSP56001",
PUBLISHER = "Motorola Inc.",
ADDRESS = "Phoenix",
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@MANUAL{LMF60DataSheet,
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PUBLISHER = "National Semiconductor Inc.",
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@MANUAL{InsideMac,
AUTHOR = "{Apple Computer Inc.}",
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ADDRESS = "Reading MA",
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@MANUAL{ADSP2105UsersManual,
AUTHOR = "{Analog Devices Inc.}",
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@MANUAL{AD1876Manual,
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@MANUAL{MatlabManual,
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AUTHOR = "{Digital Equipment Corp.}",
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@MANUAL{MC2681Manual,
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% ************************************************************
% ******* references for the Catalogs of Chaos chapter *******
@article{Molteno93,
AUTHOR = "Molteno, T.C.A.",
TITLE = "A fast $O(N)$ box counting algorithm for estimating dimensions",
JOURNAL = "Physical Review E",
VOLUME = 48,
NUMBER = 5,
YEAR = 1993,
PAGES = {3263-3266}}
@article{Mindlin92,
AUTHOR = "Mindlin, G.B. and Gilmore, R.",
TITLE = "Topological analysis and synthesis of choatic time series",
JOURNAL = "Physica D",
VOLUME = 58,
PAGES = {229-242},
YEAR = 1992}
@article{Rapp93,
AUTHOR = "Rapp, P.E. and Albano, A.M. and Schmah, T.I. and Farwell, L.A.",
TITLE = "Filtered noise can mimic low-dimensional chaotic attractors",
JOURNAL = "Physical Review E",
VOLUME = 47,
NUMBER = 4,
YEAR = 1993,
PAGES = {2289-2297}}
@article{Markus90,
AUTHOR = "Markus, M.",
TITLE = "Chaos in maps with continuous and discontinuous maxima",
JOURNAL = "Computers in Physics",
MONTH = "Sept/Oct",
YEAR = 1990,
PAGES = {481-493}}
@BOOK{Ott93,
AUTHOR = "Ott, E.",
TITLE = "Chaos in Dynamical Systems",
PUBLISHER = "Cambridge University Press",
ADDRESS = "Cambridge",
YEAR = 1993}
% *********************************************************
% ******* references for String II Results chapter *******
@article{Grebogi83,
AUTHOR = "Grebogi, C. and Ott, E. and Yorke, J.A.",
TITLE = "Crises, sudden changes in chaotic attractors, and transient chaos",
JOURNAL = "Physica D",
VOLUME = 7,
NUMBER = 1,
YEAR = 1983,
PAGES = {181-200}}