This map is a special case of the [[complex quadratic map]], which has exact solutions for many special cases.<ref>M. Little, D. Heesch (2004), [http://www.engmaxlittle.ox.ac.uk/samp/membersnet/publications/GDEA41040.pdf Chaotic root-finding for a small class of polynomials], ''Journal of Difference Equations and Applications'', '''10'''(11):949–953.</ref> The complex map obtained by raising the previous number to any natural number power <math>z_{n+1} = z_n^p </math> is also exactly solvable as <math>z_n = z_0^{p^n}</math>. In the case ''p'' = 2, the dynamics can be mapped to the dyadic transformation, as described above, but for ''p'' > 2, we obtain a shift map in the [[number base]] ''p''. For example, ''p'' = 10 is a decimal shift map.
