Iterated function systems of logistic maps: synchronization and intermittency

摘要

We discuss iterated function systems generated by finitely many logistic maps, with a focus on synchronization and intermittency. We provide sufficient conditions for synchronization, involving negative Lyapunov exponents and minimal dynamics. A number of results that clarify the scope of these conditions are included. We analyze a mechanism for intermittency that involves the full map x - 4x(1 - x) as one of the generators of the iterated function system. For iterated function systems generated by x - 2x(1 - x) and x - 4x(1 - x) we prove the existence of a sigma-finite stationary measure.