@article{PMIHES_1999__89__179_0, author = {Luzzatto, Stephano and Tucker, Warwick}, title = {Non-uniformly expanding dynamics in maps with singularities and criticalities}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {179--226}, publisher = {Institut des Hautes \'Etudes Scientifiques}, volume = {89}, year = {1999}, mrnumber = {1793416}, zbl = {0978.37029}, language = {en}, url = {http://www.numdam.org/item/PMIHES_1999__89__179_0/} }
TY - JOUR AU - Luzzatto, Stephano AU - Tucker, Warwick TI - Non-uniformly expanding dynamics in maps with singularities and criticalities JO - Publications Mathématiques de l'IHÉS PY - 1999 SP - 179 EP - 226 VL - 89 PB - Institut des Hautes Études Scientifiques UR - http://www.numdam.org/item/PMIHES_1999__89__179_0/ LA - en ID - PMIHES_1999__89__179_0 ER -
%0 Journal Article %A Luzzatto, Stephano %A Tucker, Warwick %T Non-uniformly expanding dynamics in maps with singularities and criticalities %J Publications Mathématiques de l'IHÉS %D 1999 %P 179-226 %V 89 %I Institut des Hautes Études Scientifiques %U http://www.numdam.org/item/PMIHES_1999__89__179_0/ %G en %F 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 89 (1999), pp. 179-226. http://www.numdam.org/item/PMIHES_1999__89__179_0/
[ABS77] On the appearance and structure of the Lorenz attractor, Dokl. Acad. Sci. USSR 234 (1977), 336-339. | Zbl
, and ,[BC85] On iterations of 1 - ax2 on (- 1, 1), Ann. of Math. 122 (1985), 1-25. | MR | Zbl
and ,[BC91] The dynamics of the Hénon map, Ann. of Math. 133 (1991), 73-169. | MR | Zbl
and ,[Cos98] Global strange attractors after collision of horseshoes with periodic sinks, PhD thesis, IMPA (1998).
,[dMvS93] One-dimensional dynamics, Springer Verlag, Berlin, 1993. | MR | Zbl
and ,[GW79] Structural stability of Lorenz attractors, Publ. Math. IHES 50 (1979), 59-72. | Numdam | MR | Zbl
and ,[Hén76] A two-dimensional mapping with a strange attractor, Comm. Math. Phys. 50 (1976), 69-77. | MR | Zbl
,[HL] Hyperbolicity and statistical properties of two-dimensional maps with criticalities and singularities, work in progress.
and ,[HP76] Two strange attractors with a simple structure, Lect. Notes in Math. 565 (1976), 29-68. | MR | Zbl
and ,[Jak81] Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Comm. Math. Phys. 81 (1981), 39-88. | MR | Zbl
,[Lor63] Deterministic nonperiodic flow, J. Atmosph. Sci. 20 (1963), 130-141.
,[Luz00] Bounded recurrence of critical points and Jakobson's theorem, London Mathematical Society Lecture Notes 274 (2000). | MR | Zbl
,[LV] Lorenz-like attractors without continuous invariant foliations, in preparation.
and ,[LV00] Positive Lyapunov exponents for Lorenz-like maps with criticalities, Asterisque, 261 (2000), 201-237. | Numdam | MR | Zbl
and ,[MV93] Abundance of strange attractors, Acta Math. 171 (1993), 1-71. | MR | Zbl
and ,[PRV] Persistence of global spiraling attractors, in preparation.
, , and ,[PRV98] Infinite-modal maps with global chaotic behaviour, Ann. of Math. 148 (1998), 1-44. | MR | Zbl
, , and ,[Ree86] Positive measure sets of ergodic rational maps, Ann. Sci. École Norm. Sup., 4e Série 19 (1986), 383-407. | Numdam | MR | Zbl
,[Rov93] The dynamics of perturbations of the contracting Lorenz attractor, Bull. Braz. Math. Soc. 24 (1993), 233-259. | MR | Zbl
,[Ryc88] Another proof of Jakobson's theorem and related results, Erg. Th. & Dyn. Syst. 8 (1988), 93-109. | MR | Zbl
,[Spa82] The Lorenz equations : bifurcations, chaos and strange attractors, volume 41 of Applied Mathematical Sciences, Springer Verlag, Berlin, 1982. | MR | Zbl
,[Thu98] Positive Lyapunov exponents for maps with flat critical points, Erg. Th. & Dyn. Syst. 19 (1998), 767-807. | MR | Zbl
,[Tsu93a] Positive Lyapunov exponents in families of one-dimensional dynamical systems, Inventiones Mathematicae 111 (1993), 113-137. | MR | Zbl
,[Tsu93b] A proof of Benedicks-Carleson-Jakobson Theorem, Tokyo J. Math. 16 (1993), 295-310. | MR | Zbl
,[Tuc99] The Lorenz attractor exists, C. R. Acad. Sci. Paris t. 328, Série I (1999), 1197-1202. | MR | Zbl
,[Yoc] Weakly Hyperbolic Dynamics, Birkhauser, in preparation.
,[You98] Statistical properties of dynamical systems with some hyperbolicity, Ann. of Math. 147 (1998) 585-650. | MR | Zbl
,