List of chaotic maps
2067823
211086046
2008-05-08T18:53:51Z
Adam majewski
441224
/* List of chaotic maps */ changed link from quadratic to complex quadratic polynomial/map
In [[mathematics]], a '''chaotic map''' is a [[map (mathematics)|map]] that exhibits some sort of [[chaotic behavior]]. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of [[iterated function]]s. Chaotic maps often occur in the study of [[dynamical system]]s.
Chaotic maps often generate [[fractals]]. Although a fractal may be constructed by an iterative procedure, some fractals are studied in and of themselves, as [[set (mathematics)|sets]] rather than in terms of the map that generates them. This is often because there are several different iterative procedures to generate the same fractal.
==List of chaotic maps==
* [[2x mod 1 map]] or [[Bernoulli map]] - discrete, 1D real
* [[Area-preserving maps]]
* [[Arnold's cat map]]
* [[Baker's map]] - discrete 2D real
* [[Bogdanov map]]
* [[Chossat-Golubitsky symmetry map]]
* [[Cellular automata]]
* [[Circle map]]
* [[Cob Web map]]
* [[Complex map]]
* [[Complex Cubic map]]
* [[Degenerate Double Rotor map]]
* [[Double Rotor map]]
* [[Duffing map]] - discrete, 2D real
* [[Duffing equation]] - continuous
* [[Gauss map]]
* [[Generalized Baker map]]
* [[Gingerbreadman map]]
* [[Gumowski/Mira map]]
* [[Harmonic map]]
* [[Hénon map]] - discrete 2D real
* [[Hénon with 5th order polynomial]]
* [[Hitzl-Zele map]]
* [[Horseshoe map]]
* [[Hyperbolic map]]
* [[Ikeda map]]
* [[Inclusion map]]
* [[Interval exchange map]] - discrete, 1D real
* [[Kaplan-Yorke map]] - discrete, 2D real
* [[Langton's ant]]
* [[Linear map on unit square]]
* [[Logistic map]] - discrete, 1D real
* [[Lorenz attractor]] - continuous, 3D real
* [[Lorenz system's Poincare Return map]]
* [[Lozi map]]
* [[Lyapunov fractal]]
* [[Gravity set|Mitchell-Green gravity set]]
* [[Nordmark truncated map]]
* [[Piecewise linear map]]
* [[Pullback map]]
* [[Pulsed Rotor & standard map]]
* [[Complex quadratic polynomial| Quadratic map]]
* [[Quasiperiodicity map]]
* [[Rabinovich-Fabrikant equations]] continuous, 3D real
* [[Random Rotate map]]
* [[Rössler map]] - continuous 3D real
* [[Sinai map]] - See [http://www.maths.ox.ac.uk/~mcsharry/papers/dynsys18n3p191y2003mcsharry.pdf]
* [[Symplectic map]]
* [[Standard map]]
* [[Tangent map]]
* [[Tent map]] - discrete, 1D real
* [[Tinkerbell map]]
* [[Triangle map]]
* [[Van der Pol oscillator]]
* [[Zaslavskii map]] - discrete 2D real
* [[Zaslavskii rotation map]]
<!--- Non-chaotic maps
* [[Identity map]]
--->
==List of fractals==
* [[Cantor set]]
* [[Julia set]] - discrete 1D complex
* [[Koch snowflake|Koch curve]]
* [[Mandelbrot set]] - discrete, 1D complex
* [[Menger sponge]]
* [[Sierpinski carpet]]
* [[Sierpinski triangle]]
[[Category:Chaotic maps|*]]
[[Category:Mathematics-related lists|Chaotic maps]]
[[de:Liste chaotischer Abbildungen]]