home logistic map Hénon Lorenz pendulum glossary bibliography links

Here the sources are listed which are cited on the pages before. New cites will be added to this list when new topics will be added to the glossary.



[Abarbanel96] H. D. I. Abarbanel: "Analysis of Observed Chaotic Data", Springer-Verlag Telos (1996)

[Doerner93] R. Doerner: “Die Vorhersagbarkeit von deterministisch-chaotischen Bewegungen”, Verlag Harri Deutsch 1993

[Duffing18] G. Duffing: "Erzwungene Schwingungen bei veränderlicher Eigenfrequenz", Vieweg Braunschweig (1918)

[Goldstein83] H. Goldstein: “Klassische Mechanik”, Akademische Verlagsgesellschaft Wiesbaden 1983

[Guckenheimer83] J. Guckenheimer, P.Holmes: "Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields", Springer 1983

[Hübinger93] B. Hübinger: “Die Steuerung deterministisch-chaotischer Bewegungen”, Verlag Harri Deutsch 1993

[Leiber96] Th. Leiber: “Kosmos, Kausalität und Chaos”, Reihe Spektrum Philosophie Bd.1, Ergon-Verlag 1996

[Leven89] R. W. Leven, B.-P. Koch, B. Pompe: "Chaos in dissipativen Systemen", Akademie-Verlag Berlin 1989

[Lichtenberg83] A. J. Lichtenberg, M. A. Lieberman: "Regular and Stochastic Motion", Springer-Verlag 1983

[Madan93] R. N. Madan (ed.): "Chua’s Circuit: A Paradigm for Chaos", World Scientific, Singapore, 1993

[Mandelbrot82] B. B. Mandelbrot: "The Fractal Geometry of Nature", W.H. Freeman and Company, New York 1982, bzw. B. B. Mandelbrot: "Die fraktale Geometrie der Natur", Birkhäuser 1987

[Ott93] E. Ott: "Chaos in Dynamical Systems", Cambridge 1993

[Peitgen86] H.-O. Peitgen, P. H. Richter: "The Beauty of Fractals", Springer-Verlag 1986

[Ruelle78] D. Ruelle: "Thermodynamic Formalism", Addison-Wesley 1978

[Schuster88] H. G. Schuster: "Deterministic Chaos. An Introduction", VCH Weinheim 1988, bzw. "Deterministisches Chaos. Eine Einführung", Wiley-VCH.

[Schuster99] H. G. Schuster (ed.): “Handbook of Chaos Control”, Wiley-VCH 1999

[Shannon49] C. E. Shannon, W. Weaver: "The Mathematical Theory of Information", University of Illinois Press 1949

[Sparrow82] C. Sparrow: "The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors", Springer 1982



[Abarbanel90] H. D. I. Abarbanel, R. Brown and J. B. Kadtke: "Nonlinear Prediction for Time Series with Broadband Fourier Spectra", Phys. Rev. A 41, 1782-1807 (1990)

[Abarbanel91] H. D. I. Abarbanel, R. Brown, M. B. Kennel: "Lyapunov Exponents in Chaotic Systems: their Importance and their Evaluation Using Observed Data", Int. J. Mod. Phys. B 5, 1347-1375 (1991) 

[Abarbanel91b] H. D. I. Abarbanel, R. Brown, M. B. Kennel: "Variation of Lyapunov Exponents on a Strange Attractor", J. Nonlinear Sci. 1, 175-199 (1991) 

[Alfsen85] Knut H. Alfsen, and Jan Froyland: "Systematics of the Lorenz Model at Sigma=10", Phys. Scr. 31, 15-20 (1985)

[Auerbach87] D. Auerbach, P. Cvitanovic, J.-P. Eckmann, G. Gunaratne and I. Procaccia: "Exploring chaotic motion through periodic orbits", Phys. Rev. Lett 58, 2387-2389 (1987)

[Auerbach87a] D. Auerbach, B. O’Shaugnessy and I. Procaccia: "Scaling Structure of Strange Attractors", Phys. Rev. A 37, 2234-2236 (1987)

[Broggi90] G. Broggi, R. Badii and M. Finardi: "Hierarchical Approach to Modelling of Nonlinear Flows: Application to Lorenz-Like Systems", Frühjahrstagung der S. P. G. 63, 817-818 (1990)

[Broomhead86] D. S. Broomhead and G. P. King: "Extracting Qualitative Dynamics from Experimental Data", Physica D 20, 217-236 (1986)

[Brown91] R. Brown, P. Bryant and H. D. I. Abarbanel: "Computing the Lyapunov Spectrum of a Dynamical System from an Observed Time Series", Phys. Rev. A 43, 2787-2806 (1991)

[Cvitanovic88] P. Cvitanovic: "Invariant Measurement of Strange Sets in Terms of Cycles", Phys. Rev. Lett. 61, 2729-2732 (1988)

[Doerner91] R. Doerner, B. Huebinger, W. Martienssen, S. Grossmann, and S. Thomae: "Predictability Portraits for Chaotic Motions", Chaos, Solitons & Fractals 1, 553-571 (1991)

[Doerner94] R. Doerner, B. Hübinger, H. Heng, and W. Martienssen: "Approaching nonlinear dynamics by studying the motion of a pendulum. {II}. Analyzing chaotic motion", Int. J. of Bifurcation and Chaos 4, 761-771 (1994)

[Doerner94b] R. Doerner, B. Hübinger, and W. Martienssen: "Advanced chaos forecasting", Phys. Rev. E. 50, Dez 15 (1994)

[Doerner95] R. Doerner, B. Hübinger, and W. Martienssen: "Adaptive orbit correction in chaos control", Int. J. of Bifurcation and Chaos 5, 1175-1179 (1995)

[Doerner99] R. H. Doerner: "Predictability and Local Control of Low-dimensional chaos", Handbook of Chaos Control (ed.: H.G. Schuster, Wiley-VCH) , 615-638 (1999)

[Doerner99b] R. Doerner, B.Hübinger, W. Martienssen, S. Grossmann, and S. Thomae: "Stable manifolds and predictability of dynamical systems", Chaos Solitons Fractals 10, 1759-1782 (1999)

[Dressler95] U. Dressler, T. Ritz, A. Schenck zu Schweinsberg, R. Doerner, B. Hübinger, and W. Martienssen: "Tracking unstable periodic orbits in a bronze ribbon experiment", Phys. Rev. E 51, 1845-1848 (1995)

[Epstein83] H. R. Epstein: "Oscillations and chaos in chemical systems", Physica D 7, 47 (1983)

[Epstein83b] I. Epstein, K. Kustin, P. De Kepper, M. Orban: "Oscillating Chemical Reactions", Sci. Am. 248, No.3 (1983), bzw. "Oszillierende chemische Reaktionen", Spektr. d. Wissenschaft, Mai 1983.

[Farmer87] J. D. Farmer and J. J. Sidorovic: "Predicting Chaotic Time Series", Phys. Rev. Lett. 59, 845 (1987)

[Feigenbaum78] M. J. Feigenbaum: "Quantitative universality for a class of nonlinear transformations", J. Stat. Phys. 21, 669 (1978)

[Feit78] S. D. Feit: "Characteristic exponents and strange attractors", Commun. Math. Phys. 61, 249-260 (1978)

[Franceschini81] V. Franceschini: "Stable and unstable manifolds of the Henon mapping", J. Stat. Phys. 25, 757 (1981)

[Franceschini93] V. Franceschini, C. Giberti. and Z. Zheng: "Characterization of the Lorenz Attractor by Unstable Periodic Orbits", Nonlinearity 6, 251-258 (1993)

[Frank89] G. W. Frank, T. Lookmann and M. A. H. Nerenberg: "Recovering the Attractor: a Review of Chaotic Time-Series Analysis", Can. J. Phys. 68, 711-718 (1989)

[Froyland84] J. Froyland and K. H. Alfsen: "Lyapunov-Exponent Spectra for the Lorenz Model", Phys. Rev. A 29, 2928-2931 (1984)

[Grassberger83] P. Grassberger: "Generalized Dimensions of Strange Attractors", Phys. Lett. 97A, 227 (1983)

[Grassberger83b] P. Grassberger and I. Procaccia: "Measuring the strangeness of strange attractors", Physica 9D, 189-208 (1983)

[Grassberger89] P. Grassberger, H. Kantz and U. Moenig: "On the Symbolic Dynamics of the Henon Map", J. Phys. A 22, 5217-5230 (1989)

[Grossmann77] S. Grossmann and S. Thomae: "Invariant distributions and stationary correlation functions of one-dimensional discrete processes", Z. Naturforsch. 32a, 1353 (1977)

[Gunaratne87] G. H. Gunaratne and I. Procaccia: "Organization of Chaos", Phys. Rev. Lett. 59, 1377-1380 (1987)

[Hammel85] S. Hammel, C. K. R. T. Jones and J. Maloney: "Global Dynamical Behavior of the Optical Field in a Ring Cavity", J. Opt. Soc. Am. B 2, 552 (1985)

[Heng94] H. Heng, R. Doerner, B. Hübinger and W. Martienssen: "Approaching nonlinear dynamics by studying the motion of a pendulum. {I}. Observing trajectories in state space", Int. J. of Bifurcation and Chaos 4, 751-760 (1994)

[Henon69] M. Henon, Q. Appl. Math. 27, 291 (1969)

[Henon76] M. Henon: "A two-dimensional mapping with a strange attractor", Commun. Math. Phys. 50, 69-77 (1976)

[Henon82] M. Henon: "On the numerical computation of Poincare maps", Physica D 5, 412-414 (1982)

[Hübinger93a] B. Hübinger, R. Doerner, and W. Martienssen: "Local Control of Chaotic Motion", Z. Phys. B 90, 103-106 (1993)

[Hübinger94] B. Hübinger, R. Doerner, H. Heng, and W. Martienssen: "Approaching nonlinear dynamics by studying the motion of a pendulum. {III}. Predictability and control of chaotic motion", Int. J. of Bifurcation and Chaos 4 , 773-784 (1994)

[Hübinger94a] B. Hübinger, R. Doerner, W. Martienssen, M. Herdering, R. Pitka, and U. Dressler: "Controlling Chaos in Experiments with Large Effective Lyapunov Exponents", Phys. Rev. E 50, 932 (1994)

[Jackson85] E. Atlee Jackson: "The Lorenz System: I. The Global Structure of its Stable Manifolds", Phys. Scr. 32, 469-475 (1985)

[Jackson85b] E. Atlee Jackson: "The Lorenz System: II. The Homoclinic Convolution of the Stable Manifolds", Phys. Scr. 32 , 476-481 (1985)

[Kaplan79] J. Kaplan and J. Yorke in H. O. Peitgen and H. O. Walther (ed.): "Functional Differential Equations and Approximations of Fixed Points", Springr (1979)

[Kennedy92] M. P. Kenney: "Robust OP Amp Realization of Chua’s Circuit", Frequenz 46, 66-80 (1992)

[Lathrop89] D. P. Lathrop and E. J. Kostelich: "Characterization of an Experimental Strange Attractor by Periodic Orbits", Phys. Rev. A 40, 4028-4031 (1989)

[Leonow87] G. A. Leonov, A. I. Bunin and N. Koksch: "Attraktorlokalisierung des Lorenz-Systems", Z. Angew. Math. Mech. 67, 649-656 (1987)

[Liebert89] W. Liebert and H. G. Schuster: "Proper Choice of the Time Delay for the Analysis of Chaotic Time Series", Phys. Lett. A 142, 107-111 (1989)

[Lorenz63] E. N. Lorenz: "Deterministic nonperiodic flow", J. Athmosph. Sc. 20, 130-141 (1963)

[Mackey77] M. C. Mackey and L. Glass: "Oscillation and chaos in physiological control systems", Science 197, 287-289, (1977)

[Morioka78] N. Morioka, and T. Shimizu: "Transition Between Turbulent and Periodic States in the Lorenz Model", Phys. Lett. A 66, 447-449 (1978)

[Ott90] E. Ott, C. Grebogi, J. A. Yorke: "Controlling Chaos", Phys. Rev. Lett. 64, 1196 (1990).

[Rabinovich79] M. I. Rabinovich and A. L. Fabrikant: "Stochastic self-modulation of waves in nonequilibrium media", Sov. Phys. JETP 50, 311 (1979)

[Ritz97] T. Ritz, A. Schenk zu Schweinsberg, U. Dressler, R. Doerner, B. Hübinger and W. Martienssen: "Chaos control with adjustable control times", Chaos Solitons Fractals 8, 1559-1576 (1997)

[Roessler76] O. E. Rössler:  "An equation for continuous chaos", Phys. Lett. 57A, 397 (1976)

[Roux81] J.-C. Roux, A. Rossi, S. Bachelart and C.Vidal: "Experimental observations of complex dynamics in a chemical reaction", Physica D 2, 395 (1981)

[Schwartz92] I. B. Schwartz and I. Triandaf: "Tracking Unstable Orbits in Experiments", Phys. Rev. A 46, 7439-7444 (1992)

[Schweinsberg97] A. Schenk zu Schweinsberg, T. Ritz, U. Dressler, B. Hübinger, R. Doerner and W. Martienssen: "Quasicontinuous control of a bronze ribbon experiment using time-delay coordinates", Phys. Rev. E 55, 2145-2158 (1997)

[Shimizu78] T. Shimizu and N. Morioka: "Chaos and Limit Cycles in the Lorenz Model", Phys. Lett. A 66, 182-184 (1978)

[Shimizu79] T. Shimizu: "Analytic Form of the Simplest Limit Cycle in the Lorenz Model", Physica A 97, 383-398 (1979)

[Spreuer93] H. Spreuer, and E. Adams: "On the Existence and the Verified Determination of Homoclinic and Heteroclinic Orbits of the Origin for the Lorenz Equations", Computing Suppl. 9, 233-246 (1993)

[Takens80] F. Takens: "Detecting Strange Attractors in Turbulence", in Lecture Notes in Mathematics 898, 366-381 (1980)

[Tel82] T. Tel: "On the Construction of Stable and Unstable Manifolds of Two-Dimensional Maps.", Zeitschr. Phys. B 49, 157 (1982)




mail to the author


visitors since  10/22/2000