Asymptotic measures for hyperbolic piecewise smooth mappings of a rectangle
Géométrie complexe et systèmes dynamiques - Colloque en l'honneur d'Adrien Douady Orsay, 1995, Astérisque, no. 261 (2000), pp. 103-159 
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     author = {Jakobson, Michael and Newhouse, Sheldon},
     title = {Asymptotic measures for hyperbolic piecewise smooth mappings of a rectangle},
     booktitle = {G\'eom\'etrie complexe et syst\`emes dynamiques - Colloque en l'honneur d'Adrien Douady Orsay, 1995},
     editor = {Flexor Marguerite and Sentenac Pierrette and Yoccoz Jean-Christophe},
     series = {Ast\'erisque},
     pages = {103--159},
     year = {2000},
     publisher = {Soci\'et\'e math\'ematique de France},
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     zbl = {1044.37016},
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Jakobson, Michael; Newhouse, Sheldon. Asymptotic measures for hyperbolic piecewise smooth mappings of a rectangle, dans Géométrie complexe et systèmes dynamiques - Colloque en l'honneur d'Adrien Douady Orsay, 1995, Astérisque, no. 261 (2000), pp. 103-159. https://www.numdam.org/item/AST_2000__261__103_0/

[1] R. Abraham and J. Robbin. Transversal Mappings and Flows. W. A. Benjamin, New York, N.Y., 1967. | MR | Zbl

[2] R. Adler. Afterword to R. Bowen, Invariant measures for Markov maps of the interval. Comm. Math. Phys., 69(1):1-17, 1979. | MR | Zbl | DOI

[3] V. M. Alekseev. Quasi-random dynamical systems, I. Math, of the USSR, Sbornik, 5(1):73-128, 1968. | Zbl | DOI

[4] L. Bunimovich. On a class of special flows. Math. USSR IZV., 8:219-232, 1974. | Zbl | DOI

[5] N. Friedman and D. Ornstein. On the isomorphism of weak Bernoulli transformations. Advances in Math., 5:365-394, 1970. | MR | Zbl | DOI

[6] Jack K. Hale. Ordinary Differential Equations, 2nd Ed. Krieger Publishing Co., 1980. | MR | Zbl

[7] M. Hirsch and C. Pugh. Stable manifolds and hyperbolic sets. Proc. AMS Symp. Pure Math., 14, 1970. | MR | Zbl | DOI

[8] M. V. Jakobson and S. E. Newhouse. A two dimensional version of the folklore theorem. American Math. Soc. Translations, Series 2, 171:89-105, 1996. | MR | Zbl

[9] Donald S. Ornstein. Ergodic Theory, Randomness, and Dynamical Systems. Number 5 in Yale Mathematical Monographs. Yale University Press, New Haven, Conn., 1975. | MR | Zbl

[10] C. Pugh and M. Shub. Ergodic attractors. Transactions AMS, 312(1):1-54, 1989. | MR | Zbl | DOI

[11] M. Ratner. Anosov flows with Gibbs measures are also Bernoullian. Israel J. Math., 17:380-391, 1974. | MR | Zbl | DOI

[12] M. Shub. Global Stability of Dynamical Systems. Springer-Verlag, 1987. | MR | Zbl

[13] Ya. G. Sinai. Topics in Ergodic Theory. Number 44 in Princeton Mathematical Series. Princeton University Press, 1994. | MR | Zbl

[14] Peter Walters. Invariant measures and equilibrium states for some mappings which expand distances. Trans. AMS, 236:121-153, 1978. | MR | Zbl | DOI