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.
List of chaotic maps
| Map | Time domain | Space domain | Number of space dimensions | Also known as |
|---|---|---|---|---|
| Arnold's cat map | ||||
| Baker's map | discrete | real | 2 | |
| Bogdanov map | ||||
| Chossat-Golubitsky symmetry map | ||||
| Circle map | discrete | real | 1 | |
| Cob Web map | ||||
| Complex quadratic map | discrete | complex | 1 | |
| Complex squaring map | discrete | complex | 1 | |
| Complex Cubic map | ||||
| Degenerate Double Rotor map | ||||
| Double Rotor map | ||||
| Duffing map | discrete | real | 2 | |
| Duffing equation | continuous | real | 1 | |
| Dyadic transformation | discrete | real | 1 | 2x mod 1 map, Bernoulli map, doubling map, sawtooth map |
| Exponential map | discrete | complex | 2 | |
| Generalized Baker map | ||||
| Gingerbreadman map | discrete | real | 2 | |
| Gumowski/Mira map | ||||
| Hénon map | discrete | real | 2 | |
| Hénon with 5th order polynomial | ||||
| Hitzl-Zele map | ||||
| Horseshoe map | discrete | real | 2 | |
| Ikeda map | discrete | real | 2 | |
| Interval exchange map | discrete | real | 1 | |
| Kaplan-Yorke map | discrete | real | 2 | |
| Linear map on unit square | ||||
| Logistic map | discrete | real | 1 | |
| Lorenz attractor | continuous | real | 3 | |
| Lorenz system's Poincare Return map | ||||
| Lozi map | ||||
| Nordmark truncated map | ||||
| Pulsed Rotor & standard map | ||||
| Quasiperiodicity map | ||||
| Rabinovich-Fabrikant equations | continuous | real | 3 | |
| Random Rotate map | ||||
| Rössler map | continuous | real | 3 | |
| Sinai map - See [1] | ||||
| Symplectic map | ||||
| Standard map | discrete | real | 2 | Chirikov standard map, Chirikov-Taylor map |
| Tangent map | ||||
| Tent map | discrete | real | 1 | |
| Tinkerbell map | discrete | real | 2 | |
| Triangle map | ||||
| Van der Pol oscillator | continuous | real | 1 | |
| Zaslavskii map | discrete | real | 2 | |
| Zaslavskii rotation map |
List of fractals
- Cantor set
- Gravity set, or Mitchell-Green gravity set
- Julia set - derived from complex quadratic map
- Koch snowflake
- Lyapunov fractal
- Mandelbrot set - derived from complex quadratic map
- Menger sponge
- Sierpinski carpet
- Sierpinski triangle
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