Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-21T05:17:33.361Z Has data issue: false hasContentIssue false
  • English
  • Français

Endpoints of rotation intervals for maps of the circle

Published online by Cambridge University Press:  19 September 2008

Grzegorz Świątek
Grzegorz Świątek
Affiliation:
Institute of Mathematics, Department of Mathematics, PKiN, 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.

For certain C2 one-parameter families of endomorphisms of the circle both endpoints of rotation intervals are rational except for a set of parameter values of zero Lebesgue measure.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 1 , March 1989 , pp. 173 - 190
Copyright
Copyright © Cambridge University Press 1989

References

REFERENCES

[1]Alsedá, L., Llibre, J., Misiurewicz, M. & Simó, C.. Twist periodic orbits and topological entropy for continuous maps of the circle of degree one which have a fixed point. Ergod. Th. & Dynam. Sys. 5 (1985), 501–517.CrossRefGoogle Scholar
[2]Arnold, V. I.. Small denominators, I. Mappings of the circumference onto itself. AMS Translations 2 (46) (1965), 213–284.Google Scholar
[3]Hardy, G. H. & Wright, E. M.. An Introduction to the Theory of Numbers Chapter X Oxford: Clarendom Press, 1945.Google Scholar
[4]Herman, M.. Mesure de Lebesgue et nombre de rotation, geometry and Topology. Springer Lecture Notes in Mathematics 597 (1977), 271–293.CrossRefGoogle Scholar
[5]Lanford, O. E. III. A numerical study of the likelihood of phase locking. Physica 14D (1985), 403–408.Google Scholar
[6]Misiurewicz, M.. Rotation Interval for a Class of Maps of the Real Line into Itself. Institut mittag: Leffler, Report No. 10, 1984.Google Scholar
[7]Newhouse, S., Palis, J. & Takens, F.. Bifurcations and stability of families of diffeomorphisms Publ. Mathem. IHES 57 (1983).Google Scholar