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Non-existence of wandering intervals and structure of topological attractors of one dimensional dynamical systems 2. The smooth case

Published online by Cambridge University Press:  19 September 2008

A. M. Blokh
Affiliation:
Steklov Mathematical Institute(Leningrad Department)Fontanka 27, 191011, Leningrad, USSR
M. Yu. Lyubich
Affiliation:
Steklov Mathematical Institute(Leningrad Department)Fontanka 27, 191011, Leningrad, USSR
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Abstract

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We prove that an arbitrary one dimensional smooth dynamical system with non-degenerate critical points has no wandering intervals.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1989

References

REFERENCES

[1]Lyubich, M. Yu.. Non-existence of wandering intervals and structure of topological attractors of one dimensionsl dynamical systems. I. The case of negative Schwarzian derivative. Ergod. Th. & Dyn. Sys. This issue.Google Scholar
[2]Melo, W. de & van Strien, S.. A structure theorem in one dimensional dynamics. Preprint IMPA, ser. A-063 (1986).Google Scholar
[3]van Strien, S.. Hyperbolicity and invariant measures for general C2-interval maps satisfying the Misiurewicz condition. Preprint Delft University of Technology, 87–46.Google Scholar