Tent Map

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

the name being due to the tent-like shape of the graph of f_μ. For the values of the parameter μ within 0 and 2, f_μ 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 :

where μ is a positive real constant. Choosing for instance the parameter μ=2, the effect of the function f_μ 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 x_n 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.