Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-28T03:37:11.897Z Has data issue: false hasContentIssue false
  • English
  • Français

A method for constructing attractors

Published online by Cambridge University Press:  19 September 2008

Marcy Barge
Marcy Barge
Affiliation:
Department of Mathematical Sciences, Montana State University, Bozeman, Montana 59717, USA
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.

A procedure is developed for constructing C1 diffeomorphisms of the two sphere having inverse limits of certain interval maps as attractors. The method is carried out for a particular interval map yielding a diffeomorphism with a transitive non-hyperbolic attractor.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 3 , September 1988 , pp. 331 - 349
Copyright
Copyright © Cambridge University Press 1988

References

REFERENCES

[B]Barge, M.. Horseshoe maps and inverse limits. To appear.Google Scholar
[Bi]Bing, R. H.. Snake-like continua. Duke Math. J. (3) 18 (1951), 653–663.Google Scholar
[Br]Brown, M.. Some applications of an approximation theorem for inverse limits. Proc. Amer. Math. Soc. 11 (1960), 478–483.Google Scholar
[B-M]Barge, M. & Martin, J.. The construction of global attractors, preprint available.Google Scholar
[M]Misiurewicz, M.. Embedding inverse limits of interval maps as attractors. Fund. Math. (1) 125 (1985), 23–40.Google Scholar
[S]Smale, S.. Diffeomorphisms with many periodic points. In Differential and Combinatorial Topology—A Symposium in Honor of Marston Mores, (ed. Cairns, Stewart S.), pp. 63–80. Princeton University Press: Princeton, New Jersey, 1965.Google Scholar