Abstract
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.
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.
| Original language | English |
|---|---|
| Journal | Nonlinearity |
| Volume | 28 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 8 Oct 2015 |