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Lasota-Yorke Maps With Holes: Conditionally Invariant Probability Measures And Invariant Probability Measures On The Survivor Set (2001)
| Citations: | 35 - 3 self |
BibTeX
@MISC{Liverani01lasota-yorkemaps,
author = {Carlangelo Liverani and Véronique Maume-Deschamps},
title = {Lasota-Yorke Maps With Holes: Conditionally Invariant Probability Measures And Invariant Probability Measures On The Survivor Set},
year = {2001}
}
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Abstract
Let T : I ! I 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 X1 of points which never fall into Y . Our conditions allow rather "large" holes.
