# Absolutely continuous measures for certain maps of an interval

Publications Mathématiques de l'IHÉS (1981)

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

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top## How to cite

topMisiurewicz, 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

top- [1] N. BOURBAKI, Fonctions d'une variable réelle (Livre IV), Paris, Hermann, 1958 (chap. 1, § 4, exerc. Ia).
- [2] J. GUCKENHEIMER, Sensitive dependence to initial conditions for one dimensional maps, preprint I.H.E.S. (1979). Zbl0429.58012MR82c:58037
- [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] J. MILNOR, W. THURSTON, On iterated maps of the interval, preprint. Zbl0664.58015
- [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] 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] W. PARRY, Entropy and generators in ergodic theory, New York, Benjamin, 1969. Zbl0175.34001MR41 #7071
- [8] W. PARRY, Symbolic dynamics and transformations of the unit interval, Trans. Amer. Math. Soc., 122 (1966), 368-378. Zbl0146.18604MR33 #5846
- [9] R. SHAW, Strange attractors, chaotic behavior and information flow, preprint, Santa Cruz (1978).
- [10] D. SINGER, Stable orbits and bifurcation of maps of the interval, SIAM J. Appl. Math., 35 (1978), 260-267. Zbl0391.58014MR58 #13206

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