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Graphs of maps, especially those of one variable such as the logistic map, are key to understanding the behavior of the map. One of the uses of graphs is to illustrate fixed points, called points. Draw a line y = x (a 45° line) on the graph of the map. If there is a point where this 45° line intersects with the graph, that point is a fixed point.
In mathematics, a chaotic map is a map (an 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.
Positive maps are monotone, i.e. () for all self-adjoint elements ,. Since ‖ ‖ ‖ ‖ for all self-adjoint elements , every positive map is automatically continuous with respect to the C*-norms and its operator norm equals ‖ ‖.
The Hénon map takes a point (x n, y n) in the plane and maps it to a new point {+ = + + =. The map depends on two parameters, a and b, which for the classical Hénon map have values of a = 1.4 and b = 0.3. For the classical values the Hénon map is chaotic.
Cobweb plot of the Gauss map for = and =. This shows an 8-cycle. This shows an 8-cycle. In mathematics , the Gauss map (also known as Gaussian map [ 1 ] or mouse map ), is a nonlinear iterated map of the reals into a real interval given by the Gaussian function :
An RR tachograph is a graph of the numerical value of the RR-interval versus time. In the context of RR tachography, a Poincaré plot is a graph of RR(n) on the x-axis versus RR(n + 1) (the succeeding RR interval) on the y-axis, i.e. one takes a sequence of intervals and plots each interval against the following interval. [3]
In a simple case, the intervals do not overlap and they can be inserted into a simple binary search tree and queried in () time. However, with arbitrarily overlapping intervals, there is no way to compare two intervals for insertion into the tree since orderings sorted by the beginning points or the ending points may be different.
A map is a function, as in the association of any of the four colored shapes in X to its color in Y. In mathematics, a map or mapping is a function in its general sense. [1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. [2]