Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T04:21:08.929Z Has data issue: false hasContentIssue false
  • English
  • Français

An improved real Ck Koebe principle

Published online by Cambridge University Press:  24 August 2009

SIMIN LI  and
WEIXIAO SHEN
SIMIN LI
Affiliation:
Mathematics Department, University of Science and Technology of China, Hefei, 230026, China (email: [email protected])
WEIXIAO SHEN
Affiliation:
Mathematics Department, University of Science and Technology of China, Hefei, 230026, China (email: [email protected]) Department of Mathematics, National University of Singapore, Singapore 117543, Singapore (email: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove an improved Ck Koebe principle for a Ck interval map with non-flat critical points, where k≥3, that requires no disjointness of the intervals involved.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 5 , October 2010 , pp. 1485 - 1494
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]de Faria, E. and de Melo, W.. Rigidity of critical circle mappings. I. J. Eur. Math. Soc. 1(4) (1999), 339–392.CrossRefGoogle Scholar
[2]Kozlovski, O.. How to get rid of the negative Schwarzian condition. Ann. of Math. (2) 152(3) (2000), 743–762.CrossRefGoogle Scholar
[3]de Melo, W. and van Strien, S.. One-dimensional Dynamics. Springer, Berlin, 1993.CrossRefGoogle Scholar
[4]Li, S. and Shen, W.. On C r conjugacy of S-unimodal maps. Nonlinearity 19 (2006), 1629–1634.CrossRefGoogle Scholar
[5]Li, S. and Shen, W.. Hausdorff dimension of Cantor attractors in one-dimensional dynamics. Invent. Math. 171 (2008), 345–387.CrossRefGoogle Scholar
[6]Shen, W. and Todd, M.. A C k real Koebe principle. Fund. Math. 185(1) (2005), 61–69.CrossRefGoogle Scholar
[7]Todd, M.. Distortion bounds for C 2+η unimodal maps. Fund. Math. 193 (2007), 37–77.CrossRefGoogle Scholar
[8]van Strien, S. and Vargas, E.. Real bounds, ergodicity and negative Schwarzian for multimodal maps. J. Amer. Math. Soc. 17 (2004), 749–782; 20 (2007), 267–268 (erratum).CrossRefGoogle Scholar