List of chaotic maps

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In mathematics, a chaotic map is a map (= evolution function) 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[edit]

Map Time domain Space domain Number of space dimensions Also known as
Arnold's cat map discrete real 2
Baker's map discrete real 2
Bogdanov map
Chen-Lee system continuous real 3
Chossat-Golubitsky symmetry map
Circle map discrete real 1
Complex quadratic map discrete complex 1 gives rise to the Mandelbrot set
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
Gauss map discrete real 1 mouse map, Gaussian map
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 discrete real 2
Nordmark truncated map
Pomeau-Manneville maps for intermittent chaos discrete real 1 and 2 Normal-form maps for intermittency (Types I, II and III)
Pulsed rotor
Quasiperiodicity map
Rabinovich-Fabrikant equations continuous real 3
Random Rotate map
Rössler map continuous real 3
Shobu-Ose-Mori piecewise-linear map discrete real 1 piecewise-linear approximation for Pomeau-Manneville Type I map
Sinai map - See [1]
Symplectic map
Standard map, Kicked rotor 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[edit]