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)) is intrinsically ergodic has full Lebesgue measure and we construct a set of points where intrinsic ergodicity does not hold. This paper continues the work started in [3].