On the calculation of Misiurewicz patterns in one-dimensional quadratic maps

In this work we give for the first time a table with all Misiurewicz points Mn,p for low values of the preperiod and period (2⩽n⩽8, 1⩽p⩽5) in one-dimensional quadratic maps. In the particular case of Mn,1 (important Misiurewicz points which are all placed in the period-1 chaotic band) the preperiod values are (2⩽n⩽11). A brute-force algorithm to obtain all the symbolic sequences (patterns) of the Mn,p and a more efficient algorithm to obtain the patterns of Mn,1 are also shown.