Continuity of type-I intermittency from a measure-theoretical point of view (Q1073432)

We study a simple dynamical system which displays a so-called ''type-I intermittency'' bifurcation. We determine the Bowen-Ruelle measure \(\mu_{\epsilon}\) and prove that the expectation \(\mu_{\epsilon}(g)\) of any continuous function g and the Kolmogoroff-Sinai entropy \(h(\mu_{\epsilon})\) are continuous functions of the bifurcation parameter \(\epsilon\). Therefore the transition is continuous from a measure-theoretical point of view. Those results could be generalized to any similar dynamical system.