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'')
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### 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, **, 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 .