Hostname: page-component-84b7d79bbc-c654p Total loading time: 0 Render date: 2024-07-26T18:50:10.645Z Has data issue: false hasContentIssue false
  • English
  • Français

Attracting Cantor set of positive measure for a C∞ map of an interval

Published online by Cambridge University Press:  19 September 2008

Michał Misiurewicz
Michał Misiurewicz
Affiliation:
Institute of Mathematics, Warsaw University, PKiN IX p. 00-901, Warsaw, Poland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give an example of a smooth map of an interval into itself, conjugate to the Feigenbaum map, for which the attracting Cantor set has positive Lebesgue measure.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 3-4 , December 1982 , pp. 405 - 415
Copyright
Copyright © Cambridge University Press 1982

References

REFERENCES

[1]Campanino, M. & Epstein, H.. On the existence of Feigenbaum's fixed point. Preprint I.H.E.S. 1980.Google Scholar
[2]Collet, P. & Eckmann, J.-P.. Iterated maps on the interval as dynamical systems. Progr. in Phys., vol. I, Birkhäuser: Boston, 1980.Google Scholar
[3]Feigenbaum, M. J.. Quantitative universality for a class of non-linear transformations. J. Stat. Phys. 19 (1978), 25–52.CrossRefGoogle Scholar
[4]Jonker, L.. Periodic orbits and kneading invariants. Proc. London Math. Soc. 39 (1979), 428–450.CrossRefGoogle Scholar
[5]Lanford, O. III. A computer-assisted proof of Feigenbaum conjectures. Preprint I.H.E.S. 1981.Google Scholar
[6]Misiurewicz, M.. Structure of mappings of an interval with zero entropy. Publ. I.H.E.S. 53 (1981), 5–16.Google Scholar