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

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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.

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