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1998 | 155 | 1 | 33-43
Tytuł artykułu

Topological invariance of the Collet–Eckmann property for S-unimodal maps

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that if f, g are smooth unimodal maps of the interval with negative Schwarzian derivative, conjugated by a homeomorphism of the interval, and f is Collet-Eckmann, then so is g.
Słowa kluczowe
Rocznik
Tom
155
Numer
1
Strony
33-43
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-06-03
poprawiono
1996-08-03
poprawiono
1997-03-18
poprawiono
1997-06-19
Twórcy
  • Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland, tomnow@mimuw.edu.pl
  • Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland, feliksp@impan.gov.pl
Bibliografia
  • [B1] H. Bruin, Invariant measures of interval maps, PhD thesis, Tech. Univ. Delft, 1994.
  • [B2] H. Bruin, Topological conditions for the existence of invariant measures for unimodal maps, Ergodic Theory Dynam. Systems 14 (1994), 433-452.
  • [CE] P. Collet and J.-P. Eckmann, Positive Lyapunov exponents and absolute continuity for maps of the interval, ibid. 3 (1983), 13-46.
  • [CJY] L. Carleson, P. Jones and J.-C. Yoccoz, Julia and John, Bol. Soc. Brasil. Mat. 25 (1994), 1-30.
  • [DPU] M. Denker, F. Przytycki and M. Urbański, On the transfer operator for rational functions on the Riemann sphere, Ergodic Theory Dynam. Systems 16 (1996), 255-266.
  • [GS] J. Graczyk and S. Smirnov, Collet, Eckmann, & Hölder, Invent. Math., to appear.
  • [JS] M. Jakobson and G. Świątek, Metric properties of non-renormalizable S-unimodal maps, II. Quasisymmetric conjugacy classes, Ergodic Theory Dynam. Systems 15 (1995), 871-938.
  • [M] R. Ma né, On a theorem of Fatou, Bol. Soc. Brasil. Mat. 24 (1993), 1-12.
  • [MS] W. de Melo and S. van Strien, One-Dimensional Dynamics, Springer, 1993.
  • [NP] T. Nowicki and F. Przytycki, The conjugacy of Collet-Eckmann's map of the interval with the tent map is Hölder continuous, Ergodic Theory Dynam. Systems 9 (1989), 379-388.
  • [NS] T. Nowicki and D. Sands, Nonuniform hyperbolicity and universal bounds for S-unimodal maps, Invent. Math., to appear.
  • [P1] F. Przytycki, Iterations of holomorphic Collet-Eckmann maps, conformal and invariant measures, Trans. Amer. Math. Soc., to appear.
  • [P2] F. Przytycki, On measure and Hausdorff dimension of Julia sets for holomorphic Collet-Eckmann maps, in: International Conference on Dynamical Systems, Montevideo 1995 - a Tribute to Ricardo Ma né (F. Ledrappier, J. Lewowicz and S. Newhouse, eds.), Pitman Res. Notes Math. Ser. 362, Longman, 1996, 167-181.
  • [P3] F. Przytycki, Lyapunov characteristic exponents are nonnegative, Proc. Amer. Math. Soc. 119 (1993), 309-317.
  • [P4] F. Przytycki, Hölder implies CE, Astérisque, volume dedicated to A. Douady on his 60th birthday, to appear.
  • [PR1] F. Przytycki and S. Rohde, Porosity of Collet-Eckmann Julia sets, Fund. Math., to appear.
  • [PR2] F. Przytycki and S. Rohde, Rigidity of holomorphic Collet-Eckmann repellers, preprint, May 1997.
  • [S] D. Sands, Topological conditions for positive Lyapunov exponent in unimodal case, Ph.D. thesis, St. John's College, Cambridge, 1995.
  • [SN] D. Sands and T. Nowicki, Quasisymmetric conjugacies of Collet-Eckmann maps, Ergodic Theory Dynam. Systems, to appear.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv155i1p33bwm
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