Intrinsic Ergodicity of Open dynamical systems for the doubling map

Abstract

We give sufficient conditions for intervals $(a,b)$ such that the associated open dynamical system for the doubling map is intrinsically ergodic. We also show that the set of parameters $(a,b)\in (\frac{1}{4},\frac{1}{2})\times (\frac{1}{2},\frac{3}{4})$ such that the attractor $({\Lambda }_{(a,b)},f_{(a,b)})$ is intrinsically ergodic has full Lebesgue measure and we construct a set of points where intrinsic ergodicity does not hold.

arXiv comment26 pages. This paper continues the work started in arXiv.org > math > arXiv:1506.00067