- 01-208 Carlangelo Liverani Veronique Maume-Deschamps
- Lasota-Yorke maps with holes: conditionally invariant probability
measures and invariant probability measures on the survivor set.
(376K, poscript file)
Jun 5, 01
(auto. generated ps),
of related papers
Abstract. Let T be a Lasota-Yorke map on the interval I,
let Y be a non trivial sub-interval of I and
g, 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 non absorption 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.