SRB measures for non-hyperbolic systems with multidimensional expansion
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 33 (2000) no. 1, pp. 1-32.
@article{ASENS_2000_4_33_1_1_0,
     author = {Alves, Jos\'e Ferreira},
     title = {SRB measures for non-hyperbolic systems with multidimensional expansion},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {1--32},
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     volume = {Ser. 4, 33},
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     doi = {10.1016/s0012-9593(00)00101-4},
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     zbl = {0955.37012},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/s0012-9593(00)00101-4/}
}
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Alves, José Ferreira. SRB measures for non-hyperbolic systems with multidimensional expansion. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 33 (2000) no. 1, pp. 1-32. doi : 10.1016/s0012-9593(00)00101-4. http://archive.numdam.org/articles/10.1016/s0012-9593(00)00101-4/

[1] K. Adl-Zarabi, Absolutely continuous invariant measures for piecewise expanding C2 transformations in ℝn with cusps on their boundaries, Ergodic Theory Dynamical Systems 16 (1996) 1-18. | MR | Zbl

[2] J.F. Alves, Ch. Bonatti and M. Viana, SRB measures for partially hyperbolic systems whose central direction is mostly expanding, Preprint CMUP, University of Porto, 1999.

[3] M. Benedicks and L. Carleson, On iterations of 1 - ax² on (-1, 1), Ann. Math. 122 (1985) 1-25. | MR | Zbl

[4] M. Benedicks and L. Carleson, The dynamics of the Hénon map, Ann. Math. 133 (1991) 73-169. | MR | Zbl

[5] M. Benedicks and L.-S. Young, SRB-measures for certain Hénon maps, Invent. Math. 112 (1993) 541-576. | MR | Zbl

[6] Ch. Bonatti, A. Pumariñ;O and M. Viana, Lorenz-like attractors with arbitrary unstable dimension, C. R. Acad. Sci. Série I 325 (1997) 883-888. | Zbl

[7] Ch. Bonatti and M. Viana, SRB measures for partially hyperbolic systems whose central direction is mostly contracting, Israel J. Math. (to appear). | Zbl

[8] R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows, Invent. Math. 29 (1975) 181-202. | MR | Zbl

[9] J. Buzzi, A.c.i.m.'s for arbitrary expanding piecewise ℝ-analytic mappings of the plane, Preprint Luminy, 1998.

[10] L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. | MR | Zbl

[11] E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkäuser, Basel, 1984. | MR | Zbl

[12] P. Góra and A. Boyarsky, Absolutely continuous invariant measures for piecewise expanding C2 transformations in ℝN, Israel J. Math. 67 (1989) 272-286. | MR | Zbl

[13] P. Góra and A. Boyarsky, On functions of bounded variation in higher dimensions, Amer. Math. Month. 99 (2) (1992) 159-160. | MR | Zbl

[14] M. Jakobson, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Comm. Math. Phys. 81 (1981) 39-88. | MR | Zbl

[15] G. Keller, Ergodicité et mesures invariants pour les transformations dilatants par morceaux d'une région bornée du plan, C. R. Acad. Sci. Paris Série A 289 (1979) 625-627. | MR | Zbl

[16] A. Lasota and J.A. Yorke, On the existence of invariant measures for piecewise monotonic maps, Trans. Amer. Math. Soc. 186 (1973) 481-488. | MR | Zbl

[17] R. Mañ;É, Ergodic Theory and Differentiable Dynamics, Springer, Berlin, 1987. | Zbl

[18] W. De Melo and S. Van Strien, One-Dimensional Dynamics, Springer, Berlin, 1993. | MR | Zbl

[19] L. Mora and M. Viana, Abundance of strange attractors, Acta Math. 171 (1993) 1-71. | MR | Zbl

[20] D. Ruelle, A measure associated with Axiom A attractors, Amer. J. Math. 98 (1976) 619-654. | MR | Zbl

[21] B. Saussol, Absolutely continuous invariant measures for multi-dimensional expanding maps, Preprint Luminy, 1997.

[22] Ya. Sinai, Gibbs measures in ergodic theory, Russ. Math. Surv. 27 (4) (1972) 21-69. | MR | Zbl

[23] D. Singer, Stable orbits and bifurcations of maps of the interval, SIAM J. Appl. Math. 35 (1978) 260-267. | MR | Zbl

[24] M. Tsujii, Absolutely continuous invariant measures for piecewise real-analytic maps on the plane, Preprint Hokkaido Univ., 1998.

[25] M. Viana, Strange attractors in higher dimensions, Bull. Braz. Math. Soc. 24 (1993) 13-62. | MR | Zbl

[26] M. Viana, Multidimensional nonhyperbolic attractors, Publ. Math. IHES 85 (1997) 63-96. | Numdam | MR | Zbl

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