Tent Map

In mathematics, the tent map with parameter μ is the real-valued function fμ defined by

the name being due to the tent-like shape of the graph of fμ. For the values of the parameter μ within 0 and 2, fμ maps the unit interval into itself, thus defining a discrete-time dynamical system on it (equivalently, a recurrence relation). In particular, iterating a point x0 in gives rise to a sequence :

 x_{n+1}=f_mu(x_n)=begin{cases} mu x_n & mathrm{for}~~ x_n < frac{1}{2} \ \ mu (1-x_n) & mathrm{for}~~ frac{1}{2} le x_n end{cases}

where μ is a positive real constant. Choosing for instance the parameter μ=2, the effect of the function fμ may be viewed as the result of the operation of folding the unit interval in two, then stretching the resulting interval to get again the interval . Iterating the procedure, any point x0 of the interval assumes new subsequent positions as described above, generating a sequence xn in .

The case of the tent map is a non-linear transformation of both the bit shift map and the r=4 case of the logistic map.

Read more about Tent MapBehaviour, Magnifying The Orbit Diagram, Asymmetric Tent Map

Other articles related to "tent map":

Asymmetric Tent Map
... The asymmetric tent map is essentially a distorted, but still piecewise linear, version of the case of the tent map ... The case of the tent map is the present case of ... Thus data from an asymmetric tent map cannot be distinguished, using the autocorrelation function, from data generated by a first-order autoregressive process ...

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