Gauss iterated map
Encyclopedia
In mathematics
, the Gauss map (also known as Gaussian map or mouse map), is a nonlinear iterated map of the reals
into a real interval given by the Gaussian function:
where α and β are real parameters.
Named after Johann Carl Friedrich Gauss
, the function maps the bell shaped Gaussian function similar to the logistic map
.
can be chaotic. The map is also called the mouse map because its bifurcation diagram resembles a mouse
(see Figures).
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the Gauss map (also known as Gaussian map or mouse map), is a nonlinear iterated map of the reals
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
into a real interval given by the Gaussian function:
where α and β are real parameters.
Named after Johann Carl Friedrich Gauss
Carl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...
, the function maps the bell shaped Gaussian function similar to the logistic map
Logistic map
The logistic map is a polynomial mapping of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations...
.
Properties
In the parameter space can be chaotic. The map is also called the mouse map because its bifurcation diagram resembles a mouseMouse
A mouse is a small mammal belonging to the order of rodents. The best known mouse species is the common house mouse . It is also a popular pet. In some places, certain kinds of field mice are also common. This rodent is eaten by large birds such as hawks and eagles...
(see Figures).