Misiurewicz point

Parameter in the Mandelbrot set

In mathematics, a Misiurewicz point is a parameter value in the Mandelbrot set and also in real quadratic maps of the interval for which the critical point is strictly pre-periodic. By analogy, the term Misiurewicz point is also used for parameters in a multibrot set where the unique critical point is strictly pre-periodic. This term makes less sense for maps in greater generality that have more than one free critical point because some critical points might be periodic and others not. These points are named after the Polish-American mathematician Michał Misiurewicz, who was the first to study them.

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