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Non-existence of wandering intervals and structure of topological attractors of one dimensional dynamical systems: 1. The case of negative Schwarzian derivative

Published online by Cambridge University Press:  19 September 2008

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

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It is proved that an arbitrary one dimensional dynamical system with negative Schwarzian derivative and non-degenerate critical points has no wandering intervals. This result implies a rather complete view of the dynamics of such a system. In particular, every minimal topological attractor is either a limit cycle, or a one dimensional manifold with boundary, or a solenoid. The orbit of a generic point tends to some minimal attractor.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1989

References

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