Bernoulli Convolutions and 1D Dynamics

الأصل · EN

We describe a family ϕλ of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding Bernoulli convolution will be absolutely continuous with bounded density. We study the systems ϕλ and give some numerical evidence to suggest values of λ for which ϕλ may be piecewise convex.