Dinámica de la composición polinomios de la forma zd + cn

Abstract

We study the dynamics of sequences of polynomials in P={(f_n) :f_n(z) =z^d+c_n, with (c_n) a sequence in C}. Given any sequence (f_n)∈P, we write F_n for the composition fn◦···◦f₁. We classify these sequences according to the asymptotic behavior of (F_n) and characterize such classification depending on the asymptotics of the sequence (c_n).  We generalize the results obtained by Buger and Bruck and we make a comparison between the classical iteration theory and  our  approach.   We  look  for  which  of  these  basic  results  are  preserved for any type of sequence (f_n) and in the other cases we formulate the necessary conditions for several others to be preserved.