Absolutely continuous measures for certain maps of an interval

Michal Misiurewicz

Publications Mathématiques de l'IHÉS (1981)

  • Volume: 53, page 17-51
  • ISSN: 0073-8301

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Misiurewicz, Michal. "Absolutely continuous measures for certain maps of an interval." Publications Mathématiques de l'IHÉS 53 (1981): 17-51. <http://eudml.org/doc/103973>.

@article{Misiurewicz1981,
author = {Misiurewicz, Michal},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {piecewise smooth map of an interval into itself with negative Schwarzian derivative and polynomial behaviour in the neighbourhoods of exceptional points; no periodic attracting points; existence of a probability invariant measure absolutely continuous with respect to the Lebesgue measure; metric entropies; topological entropy},
language = {eng},
pages = {17-51},
publisher = {Institut des Hautes Études Scientifiques},
title = {Absolutely continuous measures for certain maps of an interval},
url = {http://eudml.org/doc/103973},
volume = {53},
year = {1981},
}

TY - JOUR
AU - Misiurewicz, Michal
TI - Absolutely continuous measures for certain maps of an interval
JO - Publications Mathématiques de l'IHÉS
PY - 1981
PB - Institut des Hautes Études Scientifiques
VL - 53
SP - 17
EP - 51
LA - eng
KW - piecewise smooth map of an interval into itself with negative Schwarzian derivative and polynomial behaviour in the neighbourhoods of exceptional points; no periodic attracting points; existence of a probability invariant measure absolutely continuous with respect to the Lebesgue measure; metric entropies; topological entropy
UR - http://eudml.org/doc/103973
ER -

References

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  1. [1] N. BOURBAKI, Fonctions d'une variable réelle (Livre IV), Paris, Hermann, 1958 (chap. 1, § 4, exerc. Ia). 
  2. [2] J. GUCKENHEIMER, Sensitive dependence to initial conditions for one dimensional maps, preprint I.H.E.S. (1979). Zbl0429.58012MR82c:58037
  3. [3] M. JAKOBSON, Topological and metric properties of one-dimensional endomorphisms, Dokl. Akad. Nauk SSSR, 243 (1978), 866-869 (in Russian). Zbl0414.28022MR80c:28015
  4. [4] J. MILNOR, W. THURSTON, On iterated maps of the interval, preprint. Zbl0664.58015
  5. [5] M. MISIUREWICZ, Structure of mappings of an interval with zero entropy, Publ. Math. I.H.E.S., 53 (1981), 000-000. Zbl0477.58030MR83j:58071
  6. [6] M. MISIUREWICZ, W. SZLENK, Entropy of piecewise monotone mappings, Astérisque, 50 (1977), 299-310 (full version will appear in Studia Math., 67). Zbl0376.54019MR58 #7577
  7. [7] W. PARRY, Entropy and generators in ergodic theory, New York, Benjamin, 1969. Zbl0175.34001MR41 #7071
  8. [8] W. PARRY, Symbolic dynamics and transformations of the unit interval, Trans. Amer. Math. Soc., 122 (1966), 368-378. Zbl0146.18604MR33 #5846
  9. [9] R. SHAW, Strange attractors, chaotic behavior and information flow, preprint, Santa Cruz (1978). 
  10. [10] D. SINGER, Stable orbits and bifurcation of maps of the interval, SIAM J. Appl. Math., 35 (1978), 260-267. Zbl0391.58014MR58 #13206

Citations in EuDML Documents

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  1. Zbigniew Kowalski, Weakly mixing but not mixing quasi-Markovian processes
  2. Michael Benedicks, Michal Misiurewicz, Absolutely continuous invariant measures for maps with flat tops
  3. Oscar E. Lanford III, Smooth transformations of intervals
  4. Andrzej Lasota, James A. Yorke, Statistical periodicity of deterministic systems
  5. Henk Bruin, For almost every tent map, the turning point is typical
  6. A. M. Blokh, M. Yu. Lyubich, Measurable dynamics of S -unimodal maps of the interval
  7. Tomasz Nowicki, Some dynamical properties of S-unimodal maps
  8. Eduardo Colli, Marcio L. do Nascimento, Edson Vargas, Decay of geometry for Fibonacci critical covering maps of the circle
  9. P. Grzegorczyk, F. Przytycki, W. Szlenk, On iterations of Misiurewicz's rational maps on the Riemann sphere
  10. Henk Bruin, Stefano Luzzatto, Sebastian Van Strien, Decay of correlations in one-dimensional dynamics

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