“Logistic map”: an analytical solution
Savely Rabinovich, Gregory Berkolaiko, Sergey V. Buldyrev, Arkady Shekhter, Shlomo Havlin · Physica A Statistical Mechanics and its Applications · 1995
An analytical solution for the well-known quadratic recursion, the logistic map, is presented. Our derivation is based on the analogy between this recursion and a probabilistic problem that can be solved analytically. The solution is represented as a power of a transfer matrix. The proposed method allows to solve a more general quadratic mapping.