@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://archive.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://archive.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://archive.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://archive.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] Attractors of Maps of the Interval (Funct. Anal. Appl., Vol. 21, 1987, pp. 70-71 (there is a translation into English)). | Zbl
and ,[BL2] 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
and ,[BL3] Attractors of Maps of the Interval, Banach Center Publications (of the Semester on Dynamical Systems held in Warsaw, 1986), Vol. 23, 1989. | Zbl
and ,[BL4] Ergodicity of Transitive Unimodal Maps of the Interval (Ukrainian Math. J., Vol. 41, No. 7, 1989, pp. 985-988). | Zbl
and ,[BL5] Ergodic Properties of Maps of the Interval (Funct. Anal. Appl., Vol. 23, No. 1, 1989, pp. 59-60). | Zbl
and ,[BL6] 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
and ,[BL7] Measure of Solenoidal Attractors of Unimodal Maps of the Interval [Math. Notes, Vol. 48, No. 5, 1990, pp. 15-20]. | Zbl
and ,[BL8] Measure and Dimension of Solenoidal Attractors of One-Dimensional Dynamical Systems (Comm. Math. Phys., Vol. 127, 1990, pp. 573-583). | MR | Zbl
and ,[BL9] 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
and ,[CE] Iterated Maps of the Interval as Dynamical Systems, Birkhaüser, Boston, 1981.
and ,[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] Quadratic Maps Without Asymptotic Measure, Preprint, 1989.
and ,[J] Singular Measures without Restrictive Intervals (Comm. Math. Phys., Vol. 110, 1987, pp. 185-190). | MR | Zbl
,[JR] Bifurcations in One Dimension I. The Non-Wandering Set (Invent. Math., Vol. 62, 1981, pp. 347-365). | MR | Zbl
and ,[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] A Structure Theorem in One-Dimensional Dynamics, Preprint, 1986.
and ,[MMS] Julia-Fatou-Sullivan Theory for Real One-Dimensional Dynamics, Preprint, 1988.
, and ,[MMSS] Bounded Geometry and Measure of the Attracting Cantor Set of Quadratic-Like Maps, Preprint, 1988.
, , and ,[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
,Cité par Sources :