Tent map

In mathematics, the tent map with parameter μ is the real-valued function fμ defined by 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, thusdefining 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 {displaystyle x_{n}}  : 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 μ = 2 {displaystyle mu =2} 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. The tent map with parameter μ=2 and the logistic map with parameter r=4 are topologically conjugate, and thus the behaviours of the two maps are in this sense identical under iteration.