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# List of chaotic maps

### From Wikipedia, the free encyclopedia

In mathematics, a **chaotic map** is a 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 functions. Chaotic maps often occur in the study of dynamical systems.

Chaotic maps often generate fractals. Although a fractal may be constructed by an iterative procedure, some fractals are studied in and of themselves, as 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.

## [edit] 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
- Exponential map, discrete 2D complex
- 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
- Mitchell-Green gravity set
- Nordmark truncated map
- Piecewise linear map
- Pullback map
- Pulsed Rotor & standard map
- Quadratic map , discrete 2D complex
- Quasiperiodicity map
- Rabinovich-Fabrikant equations continuous, 3D real
- Random Rotate map
- Rössler map - continuous 3D real
- Sinai map - See [1]
- 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

## [edit] List of fractals

- Cantor set
- Julia set - discrete 1D complex
- Koch curve
- Mandelbrot set - discrete, 1D complex
- Menger sponge
- Sierpinski carpet
- Sierpinski triangle