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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.
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 locally convex space (E, P) with topology given by a set P of seminorms, one can define for any p ∈ P a p-contraction as a map f such that there is some k p < 1 such that p(f(x) − f(y)) ≤ k p p(x − y).
A visualization of the k-map can be considered cylindrical. The fields at edges on the left and right are adjacent, and the top and bottom are adjacent. K-Maps for four variables must be depicted as a donut or torus shape. The four corners of the square drawn by the k-map are adjacent. Still more complex maps are needed for 5 variables and more.
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]
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 :
Higher density indicates increased probability of the x variable acquiring that value for the given value of the μ parameter. The tent map with parameter μ = 2 and the logistic map with parameter r = 4 are topologically conjugate, [1] and thus the behaviours of the two maps are in this sense identical under iteration.
xy plot where x = x 0 ∈ [0, 1] is rational and y = x n for all n. The dyadic transformation (also known as the dyadic map, bit shift map, 2x mod 1 map, Bernoulli map, doubling map or sawtooth map [1] [2]) is the mapping (i.e., recurrence relation)