Non-uniformly expanding dynamics in maps with singularities and criticalities
Luzzatto, Stephano ; Tucker, Warwick
Publications Mathématiques de l'IHÉS, Tome 90 (1999), p. 179-226 / Harvested from Numdam
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@article{PMIHES_1999__89__179_0,
     author = {Luzzatto, Stefano and Tucker, Warwick},
     title = {Non-uniformly expanding dynamics in maps with singularities and criticalities},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {90},
     year = {1999},
     pages = {179-226},
     mrnumber = {2002b:37047},
     zbl = {0978.37029},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_1999__89__179_0}
}

Luzzatto, Stephano; Tucker, Warwick. Non-uniformly expanding dynamics in maps with singularities and criticalities. Publications Mathématiques de l'IHÉS, Tome 90 (1999) pp. 179-226. http://gdmltest.u-ga.fr/item/PMIHES_1999__89__179_0/

[ABS77] V. S. Afraimovich, V. V. Bykov and L. P. Shil'Nikov, On the appearance and structure of the Lorenz attractor, Dokl. Acad. Sci. USSR 234 (1977), 336-339. | Zbl 0451.76052

[BC85] M. Benedicks and L. Carleson, On iterations of 1 - ax2 on (- 1, 1), Ann. of Math. 122 (1985), 1-25. | MR 87c:58058 | Zbl 0597.58016

[BC91] M. Benedicks and L. Carleson, The dynamics of the Hénon map, Ann. of Math. 133 (1991), 73-169. | MR 92d:58116 | Zbl 0724.58042

[Cos98] M. J. Costa, Global strange attractors after collision of horseshoes with periodic sinks, PhD thesis, IMPA (1998).

[dMvS93] W. De Melo and S. Van Strien, One-dimensional dynamics, Springer Verlag, Berlin, 1993. | MR 95a:58035 | Zbl 0791.58003

[GW79] J. Guckenheimer and R. F. Williams, Structural stability of Lorenz attractors, Publ. Math. IHES 50 (1979), 59-72. | Numdam | MR 82b:58055a | Zbl 0436.58018

[Hén76] M. Hénon, A two-dimensional mapping with a strange attractor, Comm. Math. Phys. 50 (1976), 69-77. | MR 54 #10917 | Zbl 0576.58018

[HL] M. Holland and S. Luzzatto, Hyperbolicity and statistical properties of two-dimensional maps with criticalities and singularities, work in progress.

[HP76] M. Hénon and Y. Pomeau, Two strange attractors with a simple structure, Lect. Notes in Math. 565 (1976), 29-68. | MR 56 #6742 | Zbl 0379.76049

[Jak81] M. Jakobson, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Comm. Math. Phys. 81 (1981), 39-88. | MR 83j:58070 | Zbl 0497.58017

[Lor63] E. N. Lorenz, Deterministic nonperiodic flow, J. Atmosph. Sci. 20 (1963), 130-141.

[Luz00] S. Luzzatto, Bounded recurrence of critical points and Jakobson's theorem, London Mathematical Society Lecture Notes 274 (2000). | MR 2001i:37056 | Zbl 1062.37027

[LV] S. Luzzatto and M. Viana, Lorenz-like attractors without continuous invariant foliations, in preparation.

[LV00] S. Luzzatto and M. Viana, Positive Lyapunov exponents for Lorenz-like maps with criticalities, Asterisque, 261 (2000), 201-237. | MR 2001f:37036 | Zbl 0944.37025

[MV93] L. Mora and M. Viana, Abundance of strange attractors, Acta Math. 171 (1993), 1-71. | MR 94k:58089 | Zbl 0815.58016

[PRV] M. J. Pacifico, A. Rovella, and M. Viana, Persistence of global spiraling attractors, in preparation.

[PRV98] M. J. Pacifico, A. Rovella, and M. Viana, Infinite-modal maps with global chaotic behaviour, Ann. of Math. 148 (1998), 1-44. | MR 99k:58060 | Zbl 0916.58029

[Ree86] M. Rees, Positive measure sets of ergodic rational maps, Ann. Sci. École Norm. Sup., 4e Série 19 (1986), 383-407. | Numdam | MR 88g:58100 | Zbl 0611.58038

[Rov93] A. Rovella, The dynamics of perturbations of the contracting Lorenz attractor, Bull. Braz. Math. Soc. 24 (1993), 233-259. | MR 95a:58097 | Zbl 0797.58051

[Ryc88] M. Rychlik, Another proof of Jakobson's theorem and related results, Erg. Th. & Dyn. Syst. 8 (1988), 93-109. | MR 90b:58149 | Zbl 0671.58019

[Spa82] C. Sparrow, The Lorenz equations : bifurcations, chaos and strange attractors, volume 41 of Applied Mathematical Sciences, Springer Verlag, Berlin, 1982. | MR 84b:58072 | Zbl 0504.58001

[Thu98] H. Thunberg, Positive Lyapunov exponents for maps with flat critical points, Erg. Th. & Dyn. Syst. 19 (1998), 767-807. | MR 2000m:37051 | Zbl 0966.37011

[Tsu93a] M. Tsujii, Positive Lyapunov exponents in families of one-dimensional dynamical systems, Inventiones Mathematicae 111 (1993), 113-137. | MR 93j:58081 | Zbl 0787.58029

[Tsu93b] M. Tsujii, A proof of Benedicks-Carleson-Jakobson Theorem, Tokyo J. Math. 16 (1993), 295-310. | MR 94j:58104 | Zbl 0801.58027

[Tuc99] W. Tucker, The Lorenz attractor exists, C. R. Acad. Sci. Paris t. 328, Série I (1999), 1197-1202. | MR 2001b:37051 | Zbl 0935.34050

[Yoc] J.-C. Yoccoz, Weakly Hyperbolic Dynamics, Birkhauser, in preparation.

[You98] L.-S. Young, Statistical properties of dynamical systems with some hyperbolicity, Ann. of Math. 147 (1998) 585-650. | MR 99h:58140 | Zbl 0945.37009