Applications de type Lasota–Yorke à trou : mesure de probabilité conditionellement invariante et mesure de probabilité invariante sur l'ensemble des survivants

Abstract Let T :I→I be a Lasota–Yorke map on the interval I, let Y be a nontrivial sub-interval of I and g 0 :I→ R + , be a strictly positive potential which belongs to BV and admits a conformal measure m. We give constructive conditions on Y ensuring the existence of absolutely continuous (w.r.t. m) conditionally invariant probability measures to nonabsorption in Y. These conditions imply also existence of an invariant probability measure on the set X∞ of points which never fall into Y. Our conditions allow rather “large” holes.