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]]