Structure of mappings of an interval with zero entropy

Michal Misiurewicz

Publications Mathématiques de l'IHÉS (1981)

  • Volume: 53, page 5-16
  • ISSN: 0073-8301

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Misiurewicz, Michal. "Structure of mappings of an interval with zero entropy." Publications Mathématiques de l'IHÉS 53 (1981): 5-16. <http://eudml.org/doc/103975>.

@article{Misiurewicz1981,
author = {Misiurewicz, Michal},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {smooth map of an interval into itself with one critical point and with negative Schwarzian derivative; topological entropy; set of maps with positive entropy; non-wandering points; periods of periodic points; invariant Cantor set; adding machine; invariant non-atomic measure},
language = {eng},
pages = {5-16},
publisher = {Institut des Hautes Études Scientifiques},
title = {Structure of mappings of an interval with zero entropy},
url = {http://eudml.org/doc/103975},
volume = {53},
year = {1981},
}

TY - JOUR
AU - Misiurewicz, Michal
TI - Structure of mappings of an interval with zero entropy
JO - Publications Mathématiques de l'IHÉS
PY - 1981
PB - Institut des Hautes Études Scientifiques
VL - 53
SP - 5
EP - 16
LA - eng
KW - smooth map of an interval into itself with one critical point and with negative Schwarzian derivative; topological entropy; set of maps with positive entropy; non-wandering points; periods of periodic points; invariant Cantor set; adding machine; invariant non-atomic measure
UR - http://eudml.org/doc/103975
ER -

References

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  1. [1] P. COLLET, J.-P. ECKMANN, O. E. LANDFORD III, Universal properties of maps of an interval, preprint. 
  2. [2] M. FEIGENBAUM, Quantitative universality for a class of nonlinear transformation, preprint, Los Alamos. Zbl0509.58037
  3. [3] L. JONKER, Periodic orbits and kneading invariants, preprint, Warwick, June 1977. 
  4. [4] N. METROPOLIS, M. L. STEIN, P. R. STEIN, On finite limit sets for transformations on the unit interval, Journal of Combinatorial Theory (A), 15 (1973), 25-44. Zbl0259.26003MR47 #5183
  5. [5] J. MILNOR, The theory of kneading, preprint. 
  6. [6] M. MISIUREWICZ, Horsehoes for mappings of the interval, Bull. Acad. Pol. Sci., Sér. sci. math., 27 (1979), 167-169. Zbl0459.54031MR81b:58033
  7. [7] M. MISIUREWICZ, Invariant measures for continuous transformations of [0, 1] with zero topological entropy, Ergodic Theory, Proceedings, Oberwolfach, Germany, 1978, Lecture Notes in Math., 729, 144-152. Zbl0415.28015MR81a:28017
  8. [8] 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
  9. [9] D. SINGER, Stable orbits and bifurcation of maps of the interval, SIAM J. Appl. Math., 35 (1978), 260-267. Zbl0391.58014MR58 #13206
  10. [10] A. N. ŠARKOVSKIǏ, Coexistence of cycles of a continuous map of a line into itself, Ukr. Mat. Žurnal, 16 (1964), 1, 61-71 (in Russian). 
  11. [11] P. ŠTEFAN, A theorem of ŠarkovskiǏ on the existence of periodic orbits of continuous endomorphism of the real line, Commun. Math. Phys., 54 (1977), 237-248. Zbl0354.54027

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