@article{ASENS_1991_4_24_5_545_0,
author = {Blokh, A. M. and Lyubich, M. Yu.},
title = {Measurable dynamics of $S$-unimodal maps of the interval},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {545--573},
publisher = {Elsevier},
volume = {Ser. 4, 24},
number = {5},
year = {1991},
doi = {10.24033/asens.1636},
mrnumber = {93f:58132},
zbl = {0790.58024},
language = {en},
url = {http://www.numdam.org/articles/10.24033/asens.1636/}
}
TY - JOUR AU - Blokh, A. M. AU - Lyubich, M. Yu. TI - Measurable dynamics of $S$-unimodal maps of the interval JO - Annales scientifiques de l'École Normale Supérieure PY - 1991 SP - 545 EP - 573 VL - 24 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.24033/asens.1636/ DO - 10.24033/asens.1636 LA - en ID - ASENS_1991_4_24_5_545_0 ER -
%0 Journal Article %A Blokh, A. M. %A Lyubich, M. Yu. %T Measurable dynamics of $S$-unimodal maps of the interval %J Annales scientifiques de l'École Normale Supérieure %D 1991 %P 545-573 %V 24 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.24033/asens.1636/ %R 10.24033/asens.1636 %G en %F ASENS_1991_4_24_5_545_0
Blokh, A. M.; Lyubich, M. Yu. Measurable dynamics of $S$-unimodal maps of the interval. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 24 (1991) no. 5, pp. 545-573. doi : 10.24033/asens.1636. http://www.numdam.org/articles/10.24033/asens.1636/
[B1] , Decomposition of Dynamical Systems on an Interval [Russ. Math. Surveys, Vol. 38, No. 5, 1983, pp. 133-134 (translation from Russian)]. | MR | Zbl
[B2] , On the Dynamical Systems on One-Dimensional Branched Manifolds, I, II, III, (Theory of Functions, Funct. Anal. Appl. (Kharkov), Vol. 46, 1986, pp. 8-18 ; Vol. 47, 1987, pp. 67-77 ; Vol. 48, 1987, pp. 32-46). | MR | Zbl
[BL1] and , Attractors of Maps of the Interval (Funct. Anal. Appl., Vol. 21, 1987, pp. 70-71 (there is a translation into English)). | Zbl
[BL2] and , On Typical Behaviour of Trajectories of Transformations of the Interval. [Theory of Functions, Funct. Anal. Appl. (Kharkov), Vol. 49, 1988, pp. 5-15 (in Russian)]. | Zbl
[BL3] and , Attractors of Maps of the Interval, Banach Center Publications (of the Semester on Dynamical Systems held in Warsaw, 1986), Vol. 23, 1989. | Zbl
[BL4] and , Ergodicity of Transitive Unimodal Maps of the Interval (Ukrainian Math. J., Vol. 41, No. 7, 1989, pp. 985-988). | Zbl
[BL5] and , Ergodic Properties of Maps of the Interval (Funct. Anal. Appl., Vol. 23, No. 1, 1989, pp. 59-60). | Zbl
[BL6] and , On the Decomposition of One-Dimensional Dynamical Systems into Ergodic Components. (Algebra and Analysis (Leningrad Math. J.), Vol. 1, No. 1, 1989, pp. 128-145). | Zbl
[BL7] and , Measure of Solenoidal Attractors of Unimodal Maps of the Interval [Math. Notes, Vol. 48, No. 5, 1990, pp. 15-20]. | Zbl
[BL8] and , Measure and Dimension of Solenoidal Attractors of One-Dimensional Dynamical Systems (Comm. Math. Phys., Vol. 127, 1990, pp. 573-583). | MR | Zbl
[BL9] and , Non-Existence of Wandering Intervals and Structure of Topological Attractors of One-Dimensional Dynamical Systems, II. The Smooth Case (Ergodic Theor. Dynam. Syst., Vol. 9, No. 4, 1989, pp. 751-758). | Zbl
[CE] and , Iterated Maps of the Interval as Dynamical Systems, Birkhaüser, Boston, 1981.
[G1] , Sensitive Dependence to Initial Conditions for One-Dimensional Maps (Comm. Math. Phys., Vol. 70, 1979, pp. 133-160). | MR | Zbl
[G2] , Limit Sets of S-Unimodal Maps with Zero Entropy (Comm. Math. Phys., Vol. 110, 1987, pp. 655-659). | MR | Zbl
[He] , Über rein dissipative transformationen (Math. Z., Vol. 90, No. 1, 1965, pp. 41-53). | Zbl
[HK] and , Quadratic Maps Without Asymptotic Measure, Preprint, 1989.
[J] , Singular Measures without Restrictive Intervals (Comm. Math. Phys., Vol. 110, 1987, pp. 185-190). | MR | Zbl
[JR] and , Bifurcations in One Dimension I. The Non-Wandering Set (Invent. Math., Vol. 62, 1981, pp. 347-365). | MR | Zbl
[K] , Ergodic Theorems, de Gruyter Studies in Math., Vol. 6, 1985, Berlin, etc. : Walter de Gruyter. | MR | Zbl
[L1] , Measurable Dynamics of the Exponent (Syberian Math. J., Vol. 28, No. 5, 1987, pp. 111-127). | Zbl
[L2] , Non-Existence of Wandering Intervals and Structure of Topological Attractors of One-Dimensional Dynamical Systems. I. The Case of Negative Schwarzian Derivative (Ergodic Theor. Dynam. Syst., Vol. 9, No. 4, 1989, pp. 737-750). | Zbl
[Le] , Some Properties of Absolutely Continuous Invariant Measures on an Interval (Ergodic Theor. Dynam. Syst., Vol. 1, No. 1, 1981, pp. 77-93). | MR | Zbl
[M] , On the Concept of Attractor (Comm. Math. Phys., Vol. 99, 1985, pp. 177-195). | MR | Zbl
[Ma] , Hyperbolicity, Sinks and Measure in One-Dimensional Dynamics (Comm. Math. Phys., Vol. 100, 1985, pp. 495-524). | MR | Zbl
[Mi] , Structure of Mappings of the Interval with Zero Entropy (Publ. Math. I.H.E.S., Vol. 53, 1981, pp. 17-51). | Numdam | Zbl
[MS] and , A Structure Theorem in One-Dimensional Dynamics, Preprint, 1986.
[MMS] , and , Julia-Fatou-Sullivan Theory for Real One-Dimensional Dynamics, Preprint, 1988.
[MMSS] , , and , Bounded Geometry and Measure of the Attracting Cantor Set of Quadratic-Like Maps, Preprint, 1988.
[R] , The Exponential Map is Not Recurrent (Math. Z., Vol. 191, 1986, pp. 593-598). | MR | Zbl
[Ro] , Lectures on the Entropy Theory of Transformations with an Invariant Measure (Uspekhi Mat. Nauk., Vol. 22, No. 5, 1967, pp. 5-56). | MR | Zbl
[S] , Quasi Conformal Homeomorphisms and Dynamics. I. (Ann. Math., Vol. 122, 1985, pp. 401-418). | Zbl
[Si] , Stable Orbits and Bifurcations of Maps of the Interval (S.I.A.M. J. Appl. Math., Vol. 35, 1978, pp. 260-267). | MR | Zbl
[vS] , On the Bifurcatons Creating Horseshoes (Springer Lect. Notes Math., Vol. 898, 1981, pp. 316-351). | MR | Zbl
[Y] , Il n'y a pas de contre-exemple de Denjoy analytique (C.R. Acad. Sci. Paris, T. 289, Series I, 1984, pp. 141-144). | MR | Zbl
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