Teoriang chaos

Ing Teoriang chaos o Chaos theory metung yang sanga ning matematica a manigaral king pangimut da reng mapilang dynamical system a mapaliaring misnang sensitivo kareng kabilian king umpisa o initial conditions. Ining panga-sensitivo mipalaguan butterfly effect. Uli na niting panga-sensitivo, a lalto antimong daragul nang daragul a pamandagul ning pamagkamali (exponential growth of error), lalto yang balamu random (alang kapakayan o direccion) ing pangimut ning sistema. Ing buri nang sabian niti, deng mangalating pamialiwa king umpisa, magdala yang misnang dagul a pamialiwa panga-wakas, agiang king makuyad mung kapanaunan. Balamu random ing pangimut ning sistema, agiang deterministic ya iti, at ganap lang bunga o madi-determina da reng kabilian da potang purmeru deng maliliari keng paintungulan, a alang bitasang elementung random a maki papil. Ining pangimut, ausan dang deterministic chaos, o king makuyad a salita, chaos.  

Maliari ya muring akit ing pangimut a chaotic o chaotic behavior kareng sistemang natural, alimbawa king panaun (weather). Maliari yang isplica iti king metung a pamaglarawan o analysis ning chaotic mathematical model a pekakatawan ning makanian a sistema. Sisiasatan ning quantum chaos ing kaugnayan ning chaos ampong .  

 Lon la murin 

Examples of chaotic systems
 Arnold's cat map
 Bouncing Ball Simulation System
 Chua's circuit
 Double pendulum
 Dynamical billiards
 Economic bubble
 Hénon map
 Horseshoe map
 Logistic map
 Rössler attractor
 Standard map
 Swinging Atwood's machine
 Tilt A Whirl

Other related topics
 Quantum chaos
 Anosov diffeomorphism
 Bifurcation theory
 Butterfly effect
 Chaos theory in organizational development
 Complexity
 Control of chaos
 Edge of chaos
 Fractal
 Mandelbrot set
 Julia set
 Predictability
 Santa Fe Institute
 Synchronization of chaos

People
 Mitchell Feigenbaum
 Martin Gutzwiller
 Michael Berry
 Brosl Hasslacher
 Michel Hénon
 Edward Lorenz
 Aleksandr Lyapunov
 Benoît Mandelbrot
 Henri Poincaré
 Otto Rössler
 David Ruelle
 Oleksandr Mikolaiovich Sharkovsky
 Floris Takens
 James A. Yorke

 Dalerayan 

 Kasulatang cientifico 
 Articulo 
 A.N. Sharkovskii,  "Co-existence of cycles of a continuous mapping of the line into itself", Ukrainian Math. J., 16:61–71 (1964)
 Li, T. Y. and Yorke, J. A. "Period Three Implies Chaos." American Mathematical Monthly 82, 985–92, 1975.
 Kolyada, S. F. "Li-Yorke sensitivity and other concepts of chaos", Ukrainian Math. J. 56 (2004), 1242–1257.

 Libru king escuela (textbooks) 
















 Obrang semitechnical ampong popular 
 Ralph H. Abraham and Yoshisuke Ueda (Ed.), The Chaos Avant-Garde: Memoirs of the Early Days of Chaos Theory, World Scientific Publishing Company, 2001, 232 pp.
 Michael Barnsley, Fractals Everywhere, Academic Press 1988, 394 pp.
 Richard J Bird, Chaos and Life: Complexity and Order in Evolution and Thought, Columbia University Press 2003, 352 pp.
 John Briggs and David Peat, Turbulent Mirror: : An Illustrated Guide to Chaos Theory and the Science of Wholeness, Harper Perennial 1990, 224 pp.
 John Briggs and David Peat, Seven Life Lessons of Chaos: Spiritual Wisdom from the Science of Change, Harper Perennial 2000, 224 pp.
 Lawrence A. Cunningham, From Random Walks to Chaotic Crashes: The Linear Genealogy of the Efficient Capital Market Hypothesis, George Washington Law Review, Vol. 62, 1994, 546 pp.
 Leon Glass and Michael C. Mackey, From Clocks to Chaos: The Rhythms of Life, Princeton University Press 1988, 272 pp.
 James Gleick, Chaos: Making a New Science, New York: Penguin, 1988. 368 pp.
 John Gribbin, Deep Simplicity,
 L Douglas Kiel, Euel W Elliott (ed.), Chaos Theory in the Social Sciences: Foundations and Applications, University of Michigan Press, 1997, 360 pp.
 Arvind Kumar, Chaos, Fractals and Self-Organisation; New Perspectives on Complexity in Nature , National Book Trust, 2003.
 Hans Lauwerier, Fractals, Princeton University Press, 1991.
 Edward Lorenz, The Essence of Chaos, University of Washington Press, 1996.
 Chapter 5 of Alan Marshall (2002) The Unity of nature, Imperial College Press: London
 Heinz-Otto Peitgen and Dietmar Saupe (Eds.), The Science of Fractal Images, Springer 1988, 312 pp.
 Clifford A. Pickover, Computers, Pattern, Chaos, and Beauty: Graphics from an Unseen World , St Martins Pr 1991.
 Ilya Prigogine and Isabelle Stengers, Order Out of Chaos, Bantam 1984.
 Heinz-Otto Peitgen and P. H. Richter, The Beauty of Fractals : Images of Complex Dynamical Systems, Springer 1986, 211 pp.
 David Ruelle, Chance and Chaos, Princeton University Press 1993.
 Ivars Peterson, Newton's Clock: Chaos in the Solar System, Freeman, 1993.
 David Ruelle, Chaotic Evolution and Strange Attractors, Cambridge University Press, 1989.
 Peter Smith, Explaining Chaos, Cambridge University Press, 1998.
 Ian Stewart, Does God Play Dice?: The Mathematics of Chaos , Blackwell Publishers, 1990.
 Steven Strogatz, Sync: The emerging science of spontaneous order, Hyperion, 2003.
 Yoshisuke Ueda, The Road To Chaos, Aerial Pr, 1993.
 M. Mitchell Waldrop, Complexity : The Emerging Science at the Edge of Order and Chaos, Simon & Schuster, 1992.

 Suglung palual 

 Nonlinear Dynamics Research Group  with Animations in Flash
 The Chaos group at the University of Maryland
 The Chaos Hypertextbook. An introductory primer on chaos and fractals.
 Society for Chaos Theory in Psychology & Life Sciences
 Interactive live chaotic pendulum experiment , allows users to interact and sample data from a real working damped driven chaotic pendulum
 Nonlinear dynamics: how science comprehends chaos, talk presented by Sunny Auyang, 1998.
 Nonlinear Dynamics. Models of bifurcation and chaos by Elmer G. Wiens
 Gleick's Chaos (excerpt) 
 Systems Analysis, Modelling and Prediction Group  at the University of Oxford.
 A page about the Mackey-Glass equation .

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Category:Fundamental physics concepts
Category:Non-linear systems
Category:Systems
Category:Ergodic theory