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References

BBA90
P. Bryant, R. Brown, and H.D.I. Abarbanel. Lyapunov Exponents from Observed Time Series. Phys.Rev.Lett. 65(13), September 1990.

BCT90
P. Bak, K. Chen, and C. Tang. A forest-fire model and some thoughts an turbulence. Phys.Lett.A 147, 297, 1990.

BD79
A. Bjoerck and G. Dahlquist. Numerische Methoden. Oldenburg Verlag, München, 2. Auflage, 1979.

BDH90
Joseph L. Breeden, Friedrich Dinkelacker, and Alfred Hübler. Noise in the Modeling and Control of Dynamical Systems. Physical Review A 42(10), 1990.

BE91
M. Braune and H. Engel. Simulation of Autowave Propagation and Spiral Drift in Heterogeneous Excitable Media with Cellular Automata. Arbeitsbericht, Institut für physikalische Chemie, Berlin, Mai 1991.

Bes84
D. Bestle. Analyse nichtlinearer dynamischer Systeme mit qualitativen und quantitativen Methoden. Diplomarbeit, Institut B für Mechanik der Universität Stuttgart, 1984.

BH90
Joseph L. Breeden and Alfred Hübler. Reconstructing Equations of Motion from Experimental Data with Unobserved Variables. Phys. Rev. A 42, 5817--5826, November 1990.

BPV84
Pierre Bergé, Yves Pomeau, and Christian Vidal. Order within Chaos. John Wiley & Sons and Hermann, New York and Paris, 1984.

BS89
I.N. Bronstein and K.A. Semendjajew. Taschenbuch der Mathematik. Harri Deutsch, Thun und Frankfurt/Main, 24. Auflage, 1989.

BSN85
A. Babloyantz, J.M. Salazar, and C. Nicolis. Evidence of Chaotic Dynamics of Brain Activity During the Sleep Cycle. Phys. Lett. 111A, 152--156, 1985.

Bun87
H. Bunz. Zur Dynamik nichtlinearer angetriebener Oszillatoren. Dissertation, Institut für theoretische Physik und Synergetik an der Universität Stuttgart, 1987.

CE80
P. Collet and J.P. Eckmann. Iterated Maps on the Interval as Dynamical Systems. Birkhäuser, Boston, 1980.

CFPS86
J.P. Crutchfield, J.D. Farmer, N.H. Packard, and R.S. Shaw. Chaos. Scientific American 255, 38--49, 1986.

CH87
J. Cremers and A. Hübler. Construction of Differential Equations from Experimental Data. Z. Naturforsch 42a, 1987.

CHP89
Kenneth Chang, Alfred Hübler, and Norman Packard. Universal Properties of the Resonance Curve of Complex Systems. Technical Report CCSR-89-5, Center of Complex Systems Research, University of Illinois at Urbana-Champaign, 1989.

CKHJ90
K. Chang, A. Kodogeorgiou, A. Hübler, and E.A. Jackson. General Resonance Spectroscopy. Technical Report CCSR-90-19, Center of Complex Systems Research, University of Illinois at Urbana-Champaign, 1990.

CM87
J.P. Crutchfield and B.S. McNamara. Equations of Motion from a Data Series. Complex Systems 1, 417, 1987.

Coo80
N.K. Cooperrider. Nonlinear Behaviour in Rail Vehicle Dynamics, S. 173--194. S.I.A.M. Publications, Philadelphia, 1980.

Dow75
E.H. Dowell. Aeroelasticity of Plates and Shells. Noordhoff International Publishing, Leyden, 1975.

Duf18
G. Duffing. Erzwungene Schwingungen bei veränderlicher Eigenfrequenz und ihre technische Bedeutung. Vieweg, 1918.

Dyk82
Milton Van Dyke (Hrsg.). An Album of Fluid Motion. The Parabolic Press, Stanford, California, 1982.

Ebe89
Werner Eberl. Vroni sucht das absolute Maximum. Chaotische Nachrichten Nr. 3, 1989.

EHML87
W. Eberl, A. Hübler, M. Maurer, and E. Lüscher. Quasi-numerisches Näherungsverfahren zur Umwandlung von gewöhnlichen Differentialgleichungen in Differenzengleichungen. Helv. Phys. Acta 60, 1987.

EKH87
W. Eberl, M. Kuchler, A. Hübler, E. Lüscher, M. Maurer, and P. Meinke. Analytical Representation of Stroboscopic Maps of Ordinary Nonlinear Differential Equations. Z.Phys.B 68, 253--258, May 1987.

EMK83
G. Eilenberger and H. Müller-Krumbhaar (Hrsg.). Ferienkurs '83: Nichtlineare Dynamik in kondensierter Materie, Jülich, 1983. KFA Jülich GmbH.

ER85
J.P. Eckmann and D. Ruelle. Ergodic Theory of Chaos and Strange Attractors. Rev. Mod. Phys. 57, 617--56, 1985. Addendum 57, 1115.

ESGH92
W. Eberl, R. Shermer, R. Georgii, and A. Hübler. Controlling Chaos without Feedback. to be published , 1992.

ESH92
W. Eberl, H.C. Schulz, and S. Hilgenfeldt (Hrsg.). Das Chaos-Lexikon. Kunst & Alltag, München, 1992. Preprint.

Far82
J.D. Farmer. Information Dimension and the Probabilistic Structure of Chaos. Z. Naturforsch. 37a, 1304, 1982.

Fei83
M.J. Feigenbaum. Universal Behavior in Nonlinear Systems. Physica 7D, 16--39, 1983.

FS87
J.D. Farmer and J.J Sidorowich. Predicting Chaotic Time Series. Phys.Rev.Lett. 59, 845--848, 1987.

FTW83
Doyne Farmer, Tommasso Toffoli, and Steven Wolfram (Hrsg.). Cellular Automata, Amsterdam, Oxford, New York, Tokyo, März 1983. North-Holland Physics Publishing.

GEHL89
R. Georgii, W. Eberl, A. Hübler, and E. Lüscher. Resonant Stimulation and Control of Nonlinear Mechanical Pendulum by Poincaré Maps. Helv. Phys. Acta 62, 290--293, 1989.

Geo89
Robert Georgii. Nichtlineare Resonanzen. Diplomarbeit, Physik-Department E13 der TU München , 1989.

GH83
John Guckenheimer and Philip Holmes. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Applied Mathematical Sciences, Vol. 42. Springer, New York, Berlin, Heidelberg, Tokyo, 1983.

Gle88
James Gleick. Chaos -- die Ordnung des Universums. Droemer Knaur, München, 1988. engl. Original: Chaos -- Making a New Science.

Hak83
H. Haken. Synergetik--Eine Einführung. Springer, Berlin Heidelberg New York Tokyo, 1983.

Hel70
H Helmholtz. Die Lehre von den Tonempfindungen. Vieweg, 1870.

HL89
A. Hübler and E. Lüscher. Resonant Stimulation and Control of Nonlinear Oscillators. Naturwissenschaften 76, 67--69, 1989.

HL90
B.A. Huberman and E. Lumer. Dynamics of Adaptive Systems. IEEE Trans. Circuits Syst. 37(4), April 1990.

Hol87
Arun v. Holden (Hrsg.). Chaos. Manchester University Press, Manchester, 1986, paperback 1987.

HU90
John E. Hopcroft and Jeffrey D. Ullman. Einführung in die Automatentheorie, Formale Sprachen und Komplexitätstheorie. Addison-Wesley, 1990. Übersetzung der englischen Ausgabe von 1979: Introduction to Automata Theory, Languages and Computation.

Hüb87
Alfred Wilhelm Hübler. Beschreibung und Steuerung nichtlinearer Systeme. Dissertation, Physik-Department E13 der TU München , 1987.

Hüb89
A. Hübler. Adaptive Control of Chaotic Systems. Helv. Phys. Acta 62, 1989.

Hüb92
Alfred Hübler. Modeling and Control of Complex Systems: Paradigms and Applications. In L. Lam (Hrsg.), Modeling Complex Phenomena, New York, 1992. Springer Verlag.

IB84
T.E. Ingerson and R.L. Buvel. Structure in Asynchronous Cellular Automata. Physica 10D, 59--68, 1984.

IMS84
International Mathematical & Statistical Libraries, Inc., 1984. Version 9.

Jac88
A.E. Jackson. Perspectives in Nonlinear Dynamics, Band 1. Cambridge University Press, 1988.

JH90
A.E. Jackson and A. Hübler. Periodic Entrainment of Chaotic Logistic Map Dynamics. Physica 44D, 407--420, 1990.

Kan89
K. Kaneko. Spatiotemporal Chaos in One- and Two-Dimensional Coupled Map Lattices. Physica 37D, 60--82, 1989.

Kan90
K. Kaneko. Simulating Physics with Coupled Map Lattices -- Pattern Dynamics, Information Flow and Thermodynamics of Spatiotemporal Chaos. In K. Kawasaki, A. Onuki, and M. Suzuki (Hrsg.), Formation, Dynamics and Statistics of Patterns, S. 1--52. World Scientific, 1990.

Kar86
Richard M. Karp. Combinatorics, Complexity and Randomness. Communications of the ACM 29, 98, 1986.

Kau87
Thomas Kautzky. Die Konstruktion von Differentialgleichungen aus experimentellen Datensätzen. Diplomarbeit, Physik-Department E13 der TU München , München, 1987.

Kau92
Thomas Kautzky. Modellierung der Dynamik komplexer nichtlinearer Systeme. Dissertation, Physik-Department E13 der TU München , 1992.

KEHL88
M. Kuchler, W. Eberl, A. Hübler, and E. Lüscher. The Description of Complex Dynamical Systems by Simple Maps. Helv. Phys. Acta 61, 232--235, 1988.

KEHL92
M. Kuchler, W. Eberl, A Hübler, and E. Lüscher. The Calculation of Simple Maps of Complex Dynamical Systems. 1992.

KH91
S. Krempl and A. Hübler. Introduction to Optimal Control Theory of Classical and Quantum Systems. Technical Report, Center of Complex Systems Research, University of Illinois at Urbana-Champaign, März 1991.

KMIL84
T. Klinker, W. Meyer-Ilse, and W. Lauterborn. Period Doubling and Chaotic Behaviour in a Driven Toda Oscillator. Phys. Lett. A Seite 371, 1984.

Kun91
A. Kunert. Private Mitteilung, 1991.

Lie91
Wolfgang Liebert. Chaos und Herzdynamik, Band 4 von Reihe Physik. Verlag Harri Deutsch, Frankfurt am Main, 1991.

Lin81
Paul S. Linsay. Period Doubling and Chaotic Behavior in a Driven Anharmonic Oscillator. Phys.Rev.Lett. 47, 1349--1352, 1981.

LKP87
R.W. Leven, B.-P. Koch, and B. Pompe. Chaos in dissipativen Systemen. Vieweg, 1987.

LL69
Landau and Lifshitz. Lehrbuch der theoretischen Physik, Band 1, Mechanik. Akademie-Verlag, Berlin, 6. Auflage, 1969.

LL83
A.J. Lichtenberg and M.A. Lieberman. Regular and Stochastic Motion, Band 38 von Applied Mathematical Sciences. Springer, New York, Heidelberg, Berlin, 1983.

Lor63
E.N. Lorenz. Deterministic Nonperiodic Flow. J.Atmos.Sci. 20, 130, 1963.

LP88
W. Lauterborn and U. Parlitz. Methods of Chaos Physics and their Application to Acoustics. J. Acoust. Soc. Am. 84(6), 1988.

LY75
T.Y. Li and J.A. Yorke. Period Three Implies Chaos. Am. Math. Month. 82, 985--992, 1975.

MH90
M. Markus and B. Hess. Isotropic Automata for Simulations of Excitable Media: Perodicity, Chaos and Reorganization. In D. Meinköhn (Hrsg.), Dissipative Structures in Transport Processes and Combustion. Springer, 1990.

Möl90
Peter Möller. A Synergetic Model for Simulating the Activity of a Single Neuron. Vortrag im Serneus-Seminar, 8. Februar 1990.

Moo87
Francis C. Moon. Chaotic Vibrations. John Wiley & Sons, 1987.

MRP89
Thomas P. Meyer, Fred C. Richards, and Norman H. Packard. Learning Algorithm for Modeling Complex Spatial Dynamics. Phys.Rev.Lett. 63, 1735--1738, October 1989.

MWEE86
P. Möller, K. Wetzl, M. Eiswirth, and G. Ertl. Kinetic Oscillations in the Catalytic CO Oxidation on Pt(100): Computer Simulations. J. Chem. Phys. 85(9), 1986.

ND70
M. Novak and A.G. Davenport. Aeroelastcic Instability of Prisms in Turbulent Flow. In Proc. ASCE J. Eng. Mech. Div. EMI, Band 96, S. 17--39, 1970.

NM79
A.H. Nayfeh and D.T. Mook. Nonlinear Oscillations. John Wiley & Sons, New York, Chichester, Brisbane, Toronto, 1979.

OGY90
Edward Ott, Celso Grebogi, and James A. Yorke. Controlling Chaos. Technical Report, University of Maryland, College Park, MD, USA, 1989/90.

OHW90
Frank Ohle, Alfred Hübler, and Michael Welge. Adaptive Control of Chaotic Systems. Technical Report CCSR-90-13, Center of Complex Systems Research, University of Illinois at Urbana-Champaign, 1990.

Paw91
Klaus Pawelzik. Nichtlineare Dynamik und Hirnaktivität, Band 6 von Reihe Physik. Verlag Harri Deutsch, Frankfurt am Main, 1991.

PDR88
A.P. Peirce, M.A. Dahleh, and H. Rabitz. Optimal Control of Quantum--Mechanical Systems: Existence, Numerical Approximation and Applications. Phys. Rev. A 37, 4950--4964, 1988.

PFTV86
William H. Press, Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling. Numerical Recipes. Cambridge University Press, New York, New Rochelle, Melbourne, Sydney, 1986.

PH90
B. Plapp and A. Hübler. Nonlinear Resonances and Suppression of Chaos in the Rf-Biased Josephson Junction. Phys.Rev.Lett. 65, 2302--2305, 1990.

REHL88
B. Rückerl, W. Eberl, A. Hübler, and E. Lüscher. Control of the Dynamics of a Waterjet. Helv. Phys. Acta 61, 80--83, 1988.

REL89
B. Rückerl, W. Eberl, and E. Lüscher. Description of the Dynamics of Nonlinear Extended Systems by Iterative Maps. Helv. Phys. Acta 62, 347--350, 1989.

RH82
R.W. Rollins and E.R. Hunt. Exactly Solvable Model of a Physical System Exhibiting Universal Chaotic Behaviour. Phys.Rev. A 29, 3327--3334, 1982.

RHL87
G. Reiser, A. Hübler, and E. Lüscher. Algorithm for the Determination of the Resonances of Anharmonic Damped Oscillators. Z. f. Naturforschung 42a, 803--807, 1987.

RJ70
D.F. Rutland and G.J. Jameson. Droplet Production by the Disintegration of Rotating Liquid Jets. Chem. Eng. Sci. 25, 1301--1317, 1970.

RJ71
D.F. Rutland and G.J. Jameson. A Non-Linear Effect in the Capillary Instability of Liquid Jets. J.Fluid Mech. 46.2, 267--271, 1971.

Roa72
P.J. Roache. Computational Fluid Dynamics. Hermosa Publishers, 1972.

Rös76
O.E. Rössler. An Equation for Continuous Chaos. Phys.Lett. 57A, 397--8, 1976.

Rüc89
Bernhard Rückerl. Beschreibung der Dynamik ausgedehnter nichtlinearer Systeme durch Iterationsabbildungen. Diplomarbeit, Physik-Department E13 der TU München , 1989.

SB78
J. Stoer and R. Bulirsch. Einführung in die numerische Mathematik, Band 2. Springer, 1978.

Sch89a
Christian Scholz. Grippe - durchaus eine runde Sache --- A-synchron heißt nicht unzeitgemäß. Chaotische Nachrichten Nr. 1, August 1989.

Sch89b
Heinz-Georg Schuster. Deterministic Chaos. VCH-Verlagsanstalt, Weinheim, 2. Auflage, 1989.

Sch90a
Christian Scholz. Asynchrone Simulation von Systemen mit raum-zeitlicher Dynamik und Anwendung auf Datentransportprobleme. Diplomarbeit, Physik-Department E13 der TU München , 1990.

Sch90b
Hans-Christoph Schulz. Ein zellulärer Automat als Modell für die Entstehung fraktaler Strukturen bei Erosionsvorgängen. Diplomarbeit, Physik-Department E13 der TU München , 1990.

SEB90
Ch. Scholz, W. Eberl, K. Birken, S. Zaunseder, and E. Lüscher. The Influence of Asynchronous Control on the Geometry of Cellular Automaton Patterns. Helv. Phys. Acta 63, 551--552, 1990.

SH92
H.C. Schulz and S. Hilgenfeldt (Hrsg.). 25 Experimente zu Chaos und Strukturbildung. Kunst & Alltag, München, 1992.

SK89
W.-H. Steeb and A. Kunick. Chaos in Dynamischen Systemen. Bibliographisches Institut, Mannheim, 2. Auflage, 1989.

SKL90
H.C. Schulz, T. Kautzky, and E. Lüscher. A Model for the Pattern Formation due to Erosion. Helv. Phys. Acta 63, 535--537, 1990.

SRR90
S. Sinha, R. Ramaswamy, and J.S. Rao. Adaptive Control in Nonlinear Systems. Physica 43D, 118--128, 1990.

Ste91
Willi-Hans Steeb. A Handbook of Terms Used in Chaos and Quantum Chaos. BI Wissenschaftsverlag, Mannheim, 1991.

Swi83
H.L. Swinney. Observations of Order and Chaos in Nonlinear Systems. Physica 7D, 3--15, 1983.

TEH90
V. Thurner, W. Eberl, A. Hübler, N. Packard, and E. Lüscher. Determination of the Absolute Maximum of Polynomials by Algebraic Bisection. Helv. Phys. Acta 63, 549--550, 1990.

TEH91
V. Thurner, W. Eberl, and A. Hübler. Determination of the Absolute Maximum of Polynomials by Algebraic Bisection Method. Technical Report, Center of Complex Systems Research, University of Illinois at Urbana-Champaign, 1991.

TH88
Pablo Tamayo and Hyman Hartman. Cellular Automata, Reaction-Diffusion Systems and the Origin of Life. In C. Langton (Hrsg.), Artificial Life, SFI Studies in the Sciences of Complexity, S. 105--124. Addison-Wesley, 1988.

TM87
T. Toffoli and N. Margolus. Cellular Automata Machine. MIT Press, 1987.

TPJ82
J. Testa, J. Pérez, and C. Jeffries. Evidence for Universal Chaotic Behavior of a Driven Nonlinear Oscillator. Phys.Rev.Lett. 48, 714--717, 1982.

URP74
A. Uppal, W.H. Ray, and A. Poore. On the Dynamic Behaviour of Continous Stirred Tank Reactors. Chem. Eng. Sci. 29, 967--985, 1974.

Wan89
Andreas Wandelt. Anwendung von Normalzeittransformationen zur analytischen Berechnung von Poincaré-Abbildungen. Diplomarbeit, Physik-Department E13 der TU München , 1989.

WEHL88
R. Wackerbauer, W. Eberl, A. Hübler, and E. Lüscher. Analytical Representation of Stroboscopic Maps of Ordinary Nonlinear Differential Equations. Helv. Phys. Acta 61, 236--239, 1988.

WEHL89
A. Wandelt, W. Eberl, A. Hübler, and E. Lüscher. Transformation to Normal Time for the Calculation of Poincaré Maps in Closed Form. Helv. Phys. Acta 62, 339--342, 1989.

WHMK92
Renate Wackerbauer, Alfred Hübler, and Gottfried Mayer-Kress. Algebraic Calculation of Stroboscopic Maps of Ordinary, Nonlinear Differential Equations. to appear in Physica D , 1992.

Win74
A.T. Winfree. Rotating Chemical Reactions. Sci.Am. 230, 82--95, June 1974.

WKHL91
R. Wittmann, T. Kautzky, A. Hübler, and E. Lüscher. A simple Experiment for the Examination of Dendritic River Systems. Naturwissenschaften 78, 23--25, 1991.

Wol86
Stephen Wolfram. Theory and Applications of Cellular Automata. World Scientific, 1986.

Wor92
R. Worg. Nichtlineare Dynamik: Didaktische Studien zu einem neuen Teilbereich der Physik. Dissertation, Ludwig-Maximilians-Universität, München, 1991/92.

WSHL88
C. Wagner, W. Stelzel, A. Hübler, and E. Lüscher. Resonante Steuerung nichtlinearer Schwinger. Helv. Phys. Acta 61, 228--231, 1988.

Zen92
Ch. Zenger. private Mitteilung, Januar 1992.



Werner Eberl
Fri Apr 14 00:36:50 MET DST 1995