Measurable dynamics of S-unimodal maps of the interval
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 24 (1991) no. 5, pp. 545-573.
@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, Serie 4, Volume 24 (1991) no. 5, pp. 545-573. doi : 10.24033/asens.1636. http://www.numdam.org/articles/10.24033/asens.1636/

[B1] A. M. Blokh, Decomposition of Dynamical Systems on an Interval [Russ. Math. Surveys, Vol. 38, No. 5, 1983, pp. 133-134 (translation from Russian)]. | MR | Zbl

[B2] A. M. Blokh, 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] A. M. Blokh and M. Yu. Lyubich, Attractors of Maps of the Interval (Funct. Anal. Appl., Vol. 21, 1987, pp. 70-71 (there is a translation into English)). | Zbl

[BL2] A. M. Blokh and M. Yu. Lyubich, 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] A. M. Blokh and M. Yu. Lyubich, Attractors of Maps of the Interval, Banach Center Publications (of the Semester on Dynamical Systems held in Warsaw, 1986), Vol. 23, 1989. | Zbl

[BL4] A. B. Blokh and M. Yu. Lyubich, Ergodicity of Transitive Unimodal Maps of the Interval (Ukrainian Math. J., Vol. 41, No. 7, 1989, pp. 985-988). | Zbl

[BL5] A. M. Blokh and M. Yu. Lyubich, Ergodic Properties of Maps of the Interval (Funct. Anal. Appl., Vol. 23, No. 1, 1989, pp. 59-60). | Zbl

[BL6] A. M. Blokh and M. Yu. Lyubich, 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] A. M. Blokh and M. Yu Lyubich, Measure of Solenoidal Attractors of Unimodal Maps of the Interval [Math. Notes, Vol. 48, No. 5, 1990, pp. 15-20]. | Zbl

[BL8] A. M. Blokh and M. Yu. Lyubich, Measure and Dimension of Solenoidal Attractors of One-Dimensional Dynamical Systems (Comm. Math. Phys., Vol. 127, 1990, pp. 573-583). | MR | Zbl

[BL9] A. M. Blokh and M. Yu. Lyubich, 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] P. Collet and J.-P. Eckmann, Iterated Maps of the Interval as Dynamical Systems, Birkhaüser, Boston, 1981.

[G1] J. Guckenheimer, Sensitive Dependence to Initial Conditions for One-Dimensional Maps (Comm. Math. Phys., Vol. 70, 1979, pp. 133-160). | MR | Zbl

[G2] J. Guckenheimer, Limit Sets of S-Unimodal Maps with Zero Entropy (Comm. Math. Phys., Vol. 110, 1987, pp. 655-659). | MR | Zbl

[He] Von G. Helmberg, Über rein dissipative transformationen (Math. Z., Vol. 90, No. 1, 1965, pp. 41-53). | Zbl

[HK] F. Hofbauer and G. Keller, Quadratic Maps Without Asymptotic Measure, Preprint, 1989.

[J] S. Johnson, Singular Measures without Restrictive Intervals (Comm. Math. Phys., Vol. 110, 1987, pp. 185-190). | MR | Zbl

[JR] L. Jonker and D. Rand, Bifurcations in One Dimension I. The Non-Wandering Set (Invent. Math., Vol. 62, 1981, pp. 347-365). | MR | Zbl

[K] U. Krengel, Ergodic Theorems, de Gruyter Studies in Math., Vol. 6, 1985, Berlin, etc. : Walter de Gruyter. | MR | Zbl

[L1] M. Yu. Lyubich, Measurable Dynamics of the Exponent (Syberian Math. J., Vol. 28, No. 5, 1987, pp. 111-127). | Zbl

[L2] M. Yu. Lyubich, 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] F. Ledrappier, 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] J. Milnor, On the Concept of Attractor (Comm. Math. Phys., Vol. 99, 1985, pp. 177-195). | MR | Zbl

[Ma] R. Mañ;E, Hyperbolicity, Sinks and Measure in One-Dimensional Dynamics (Comm. Math. Phys., Vol. 100, 1985, pp. 495-524). | MR | Zbl

[Mi] Misiurewicz, Structure of Mappings of the Interval with Zero Entropy (Publ. Math. I.H.E.S., Vol. 53, 1981, pp. 17-51). | Numdam | Zbl

[MS] W. De Melo and S. J. Van Strien, A Structure Theorem in One-Dimensional Dynamics, Preprint, 1986.

[MMS] M. Martens, W. De Melo and S. J. Van Strien, Julia-Fatou-Sullivan Theory for Real One-Dimensional Dynamics, Preprint, 1988.

[MMSS] M. Martens, W. De Melo, S. J. Van Strien and D. Sullivan, Bounded Geometry and Measure of the Attracting Cantor Set of Quadratic-Like Maps, Preprint, 1988.

[R] M. Rees, The Exponential Map is Not Recurrent (Math. Z., Vol. 191, 1986, pp. 593-598). | MR | Zbl

[Ro] V. A. Rokhlin, 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] S. Sullivan, Quasi Conformal Homeomorphisms and Dynamics. I. (Ann. Math., Vol. 122, 1985, pp. 401-418). | Zbl

[Si] D. Singer, 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] S. J. Van Strien, On the Bifurcatons Creating Horseshoes (Springer Lect. Notes Math., Vol. 898, 1981, pp. 316-351). | MR | Zbl

[Y] J.-C. Yoccoz, 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

Cited by Sources: