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1993 | 142 | 1 | 45-57
Tytuł artykułu

Some dynamical properties of S-unimodal maps

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study 1) the slopes of central branches of iterates of S-unimodal maps, comparing them to the derivatives on the critical trajectory, 2) the hyperbolic structure of Collet-Eckmann maps estimating the exponents, and under a summability condition 3) the images of the density one under the iterates of the Perron-Frobenius operator, 4) the density of the absolutely continuous invariant measure.
Słowa kluczowe
Rocznik
Tom
142
Numer
1
Strony
45-57
Opis fizyczny
Daty
wydano
1993
otrzymano
1991-09-02
poprawiono
1992-06-08
Twórcy
  • Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
  • [BL] A. Blokh and M. Lyubich, Measurable dynamics of S-unimodal maps of the interval, Ann. Sci. École Norm. Sup. 24 (1991), 545-573.
  • [CE1] P. Collet and J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Birkhäuser, Boston 1980.
  • [CE2] P. Collet and J.-P. Eckmann, Positive Liapounov exponents and absolute continuity for maps of the interval, Ergodic Theory Dynamical Systems 3 (1983), 13-46.
  • [K] G. Keller, Exponents, attractors and Hopf decomposition for interval maps, ibid. 10 (1990), 717-744.
  • [KN] G. Keller and T. Nowicki, Spectral theory, zeta functions and the distribution of periodic points for the Collet-Eckmann maps, Comm. Math. Phys. 149 (1992), 31-69.
  • [L] F. Ledrappier, Some properties of absolutely continuous invariant measures on an interval, Ergodic Theory Dynamical Systems 1 (1981), 77-93.
  • [MS] W. de Melo and S. van Strien, One Dimensional Dynamic, book manuscript.
  • [M] M. Misiurewicz, Absolutely continuous invariant measures for certain maps of an interval, Publ. Math. I.H.E.S. 53 (1981), 17-51.
  • [N1] T. Nowicki, On some dynamical properties of S-unimodal maps of an interval, Fund. Math. 126 (1985), 27-43.
  • [N2] T. Nowicki, Symmetric S-unimodal mappings and positive Liapunov exponents, Ergodic Theory Dynamical Systems 5 (1985), 611-616.
  • [N3] T. Nowicki, A positive Liapunov exponent for the critical value of an S-unimodal mapping implies uniform hyperbolicity, ibid. 8 (1988), 425-435.
  • [NS1] T. Nowicki and S. van Strien, Hyperbolicity properties of multimodal Collet-Eckmann maps without Schwarzian derivative conditions, Trans. Amer. Math. Soc. 321 (1990), 793-810.
  • [NS2] T. Nowicki and S. van Strien, Absolutely continuous invariant measures for $C^2$ unimodal maps satisfying Collet-Eckmann conditions, Invent. Math. 93 (1988), 619-635.
  • [NS3] T. Nowicki and S. van Strien, Invariant measures exist under a summability condition for unimodal maps, ibid. 105 (1991), 123-136.
  • [Sz] B. Szewc, Perron-Frobenius operator in spaces of smooth functions on an interval, Ergodic Theory Dynamical Systems 4 (1984), 613-641.
  • [Y] L.-S. Young, Decay of correlations for certain quadratic maps, Comm. Math. Phys. 146 (1992), 123-138.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv142i1p45bwm
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