Measurable dynamics of -unimodal maps of the interval
Annales scientifiques de l'École Normale Supérieure (1991)
- Volume: 24, Issue: 5, page 545-573
- ISSN: 0012-9593
Access Full Article
topHow to cite
topBlokh, A. M., and Lyubich, M. Yu.. "Measurable dynamics of $S$-unimodal maps of the interval." Annales scientifiques de l'École Normale Supérieure 24.5 (1991): 545-573. <http://eudml.org/doc/82305>.
@article{Blokh1991,
author = {Blokh, A. M., Lyubich, M. Yu.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {one-dimensional measurable dynamics; S-unimodal map; interval; attractors; Cantor attractors},
language = {eng},
number = {5},
pages = {545-573},
publisher = {Elsevier},
title = {Measurable dynamics of $S$-unimodal maps of the interval},
url = {http://eudml.org/doc/82305},
volume = {24},
year = {1991},
}
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
PB - Elsevier
VL - 24
IS - 5
SP - 545
EP - 573
LA - eng
KW - one-dimensional measurable dynamics; S-unimodal map; interval; attractors; Cantor attractors
UR - http://eudml.org/doc/82305
ER -
References
top- [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)]. Zbl0557.28017MR86d:54060
- [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). Zbl0701.58022MR89i:58057
- [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)). Zbl0653.58022
- [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)]. Zbl0666.58031
- [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. Zbl0698.58037
- [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). Zbl0774.58018
- [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). Zbl0704.58015
- [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). Zbl0718.58024
- [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]. Zbl0774.58026
- [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). Zbl0721.58033MR91g:58164
- [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). Zbl0665.58024
- [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). Zbl0429.58012MR82c:58037
- [G2] J. GUCKENHEIMER, Limit Sets of S-Unimodal Maps with Zero Entropy (Comm. Math. Phys., Vol. 110, 1987, pp. 655-659). Zbl0625.58027MR88i:58111
- [He] Von G. HELMBERG, Über rein dissipative transformationen (Math. Z., Vol. 90, No. 1, 1965, pp. 41-53). Zbl0178.38701
- [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). Zbl0641.58024MR88g:58093
- [JR] L. JONKER and D. RAND, Bifurcations in One Dimension I. The Non-Wandering Set (Invent. Math., Vol. 62, 1981, pp. 347-365). Zbl0475.58014MR83d:58057a
- [K] U. KRENGEL, Ergodic Theorems, de Gruyter Studies in Math., Vol. 6, 1985, Berlin, etc. : Walter de Gruyter. Zbl0575.28009MR87i:28001
- [L1] M. Yu. LYUBICH, Measurable Dynamics of the Exponent (Syberian Math. J., Vol. 28, No. 5, 1987, pp. 111-127). Zbl0667.58037
- [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). Zbl0665.58023
- [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). Zbl0487.28015MR82k:28018
- [M] J. MILNOR, On the Concept of Attractor (Comm. Math. Phys., Vol. 99, 1985, pp. 177-195). Zbl0595.58028MR87i:58109a
- [Ma] R. MAÑ;E, Hyperbolicity, Sinks and Measure in One-Dimensional Dynamics (Comm. Math. Phys., Vol. 100, 1985, pp. 495-524). Zbl0583.58016MR87f:58131
- [Mi] MISIUREWICZ, Structure of Mappings of the Interval with Zero Entropy (Publ. Math. I.H.E.S., Vol. 53, 1981, pp. 17-51). Zbl0477.58030
- [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). Zbl0595.30033MR87g:58063
- [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). Zbl0174.45501MR36 #349
- [S] S. SULLIVAN, Quasi Conformal Homeomorphisms and Dynamics. I. (Ann. Math., Vol. 122, 1985, pp. 401-418). Zbl0589.30022
- [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). Zbl0391.58014MR58 #13206
- [vS] S. J. van STRIEN, On the Bifurcatons Creating Horseshoes (Springer Lect. Notes Math., Vol. 898, 1981, pp. 316-351). Zbl0491.58023MR83h:58072
- [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). Zbl0573.58023MR85j:58134
Citations in EuDML Documents
top- Viviane Baladi, Marcelo Viana, Strong stochastic stability and rate of mixing for unimodal maps
- Artur Avila, Carlos Gustavo Moreira, Statistical properties of unimodal maps
- Viviane Baladi, Michael Benedicks, Véronique Maume-Deschamps, Almost sure rates of mixing for i.i.d. unimodal maps
- Tomasz Nowicki, Some dynamical properties of S-unimodal maps
- Henk Bruin, Stefano Luzzatto, Sebastian Van Strien, Decay of correlations in one-dimensional dynamics
- Neil Dobbs, On cusps and flat tops
- Henk Bruin, Weixiao Shen, Sebastian Van Strien, Existence of unique SRB-measures is typical for real unicritical polynomial families
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.