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

Tomasz Nowicki; Feliks Przytycki

Fundamenta Mathematicae (1998)

- Volume: 155, Issue: 1, page 33-43
- ISSN: 0016-2736

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topNowicki, Tomasz, and Przytycki, Feliks. "Topological invariance of the Collet–Eckmann property for S-unimodal maps." Fundamenta Mathematicae 155.1 (1998): 33-43. <http://eudml.org/doc/212241>.

@article{Nowicki1998,

abstract = {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.},

author = {Nowicki, Tomasz, Przytycki, Feliks},

journal = {Fundamenta Mathematicae},

keywords = {-unimodal maps; absolutely continuous invariant measure; Collet-Eckmann condition; topological invariants; topological conjugacy; holomorphic dynamics},

language = {eng},

number = {1},

pages = {33-43},

title = {Topological invariance of the Collet–Eckmann property for S-unimodal maps},

url = {http://eudml.org/doc/212241},

volume = {155},

year = {1998},

}

TY - JOUR

AU - Nowicki, Tomasz

AU - Przytycki, Feliks

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

JO - Fundamenta Mathematicae

PY - 1998

VL - 155

IS - 1

SP - 33

EP - 43

AB - 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.

LA - eng

KW - -unimodal maps; absolutely continuous invariant measure; Collet-Eckmann condition; topological invariants; topological conjugacy; holomorphic dynamics

UR - http://eudml.org/doc/212241

ER -

## References

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- [P1] F. Przytycki, Iterations of holomorphic Collet-Eckmann maps, conformal and invariant measures, Trans. Amer. Math. Soc., to appear. Zbl0892.58063
- [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. Zbl0787.58037
- [P4] F. Przytycki, Hölder implies CE, Astérisque, volume dedicated to A. Douady on his 60th birthday, to appear.
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- [PR2] F. Przytycki and S. Rohde, Rigidity of holomorphic Collet-Eckmann repellers, preprint, May 1997. Zbl1034.37026
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- [SN] D. Sands and T. Nowicki, Quasisymmetric conjugacies of Collet-Eckmann maps, Ergodic Theory Dynam. Systems, to appear.

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