Lasota-Yorke maps with holes : conditionally invariant probability measures and invariant probability measures on the survivor set
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 3, pp. 385-412. 
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     author = {Liverani, Carlangelo and Maume-Deschamps, V\'eronique},
     title = {Lasota-Yorke maps with holes : conditionally invariant probability measures and invariant probability measures on the survivor set},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {385--412},
     publisher = {Elsevier},
     volume = {39},
     number = {3},
     year = {2003},
     doi = {10.1016/S0246-0203(02)00005-5},
     zbl = {1021.37002},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S0246-0203(02)00005-5/}
}
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Liverani, Carlangelo; Maume-Deschamps, Véronique. Lasota-Yorke maps with holes : conditionally invariant probability measures and invariant probability measures on the survivor set. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 3, pp. 385-412. doi : 10.1016/S0246-0203(02)00005-5. http://www.numdam.org/articles/10.1016/S0246-0203(02)00005-5/

[1] H. van den Bedem, N. Chernov, Expanding maps of an interval with holes, Preprint. | MR | Zbl

[2] G. Birkhoff, Lattice Theory, A.M.S. Colloq. Publ., Providence, 1967. | MR | Zbl

[3] V. Baladi, G. Keller, Zeta functions and transfer operator for piecewise monotone transformations, Comm. Math. Phys. 127 (1990) 459-477. | MR | Zbl

[4] N. Chernov, R. Markarian, S. Troubetzkoy, Conditionally invariant measures for Anosov maps with small holes, Ergodic Theory Dynam. Systems 18 (5) (1998) 1049-1073. | MR | Zbl

[5] P. Collet, Ergodic properties of maps of the interval, in: Bamon R., Gambaudo J.-M., Martínez S. (Eds.), Dynamical Systems, Hermann, 1996. | MR | Zbl

[6] P. Collet, S. Martínez, B. Schmitt, The Pianigiani-Yorke measure for topological Markov chains, Israel J. Math. 97 (1997) 61-70. | MR | Zbl

[7] P. Collet, S. Martínez, B. Schmitt, The Pianigiani-Yorke measure and the asymptotic law on the limit Cantor set of expanding systems, Nonlinearity 7 (1994) 1437-1443. | MR | Zbl

[8] P. Collet, S. Martínez, B. Schmitt, Quasi-stationary distribution and Gibbs measure of expanding systems, Instabilities and Non-Equilibrium Structures (1996) 205-219. | MR | Zbl

[9] P. Collet, S. Martínez, V. Maume-Deschamps, On the existence of conditionally invariant measures in dynamical systems, Nonlinearity 13 (2000) 1263-1274. | MR | Zbl

[10] P.A. Ferrari, H. Kesten, S. Martínez, P. Picco, Existence of quasi-stationary distributions. A renewal dynamical approach, Ann. Probab. 23 (1995) 501-521. | MR | Zbl

[11] P. Ferrero, B. Schmitt, Ruelle's Perron-Frobenius theorem and projective metrics, Coll. Math. Soc. J. Bollyai 27 (1979).

[12] G. Keller, Markov extensions, zeta functions, and Fredholm theory for piecewise invertible dynamical systems, Trans. Amer. Math. Soc. 314 (2) (1989) 433-497. | MR | Zbl

[13] G. Keller, C. Liverani, Stability of the Spectral Gap for transfer operators, Annali della Scuola Normale di Pisa, Classe di Scienze (4) XXVIII (1999) 141-152. | Numdam | MR | Zbl

[14] C. Liverani, Decay of correlations, Ann. of Math. 142 (2) (1995) 239-301. | MR | Zbl

[15] C. Liverani, Decay of correlations for piecewise expanding maps, J. Statist. Phys. 78 (3-4) (1995) 1111-1129. | Zbl

[16] C. Liverani, B. Saussol, S. Vaienti, Conformal measure and decay of correlations for covering weighted systems, Ergodic Theory Dynam. Systems 18 (6) (1998) 1399-1420. | MR | Zbl

[17] G. Pianigiani, J.A. Yorke, Expanding maps on sets which are almost invariant: decay and chaos, Trans. Amer. Math. Soc. 252 (1989) 433-497. | MR | Zbl

[18] M. Rychlik, Bounded variation and invariant measures, Studia Math. 71 (1982) 69-80. | MR | Zbl

[19] D. Vere-Jones, Geometric ergodicity in denumerable Markov chains, Quart. J. Math. 13 (2) (1962) 7-28. | MR | Zbl

[20] M. Viana, Stochastic dynamics of deterministic systems, Brazillian Math. Colloquium, IMPA, 1997.

[21] L.-S. Young, Dimension, entropy and Lyapunov exponents, Ergodic Theory Dynam. Systems 2 (1982) 109-124. | MR | Zbl

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