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Rotation shadowing properties of circle and annulus maps

Published online by Cambridge University Press:  19 September 2008

Marcy Barge  and
Richard Swanson
Marcy Barge
Affiliation:
Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, USA
Richard Swanson
Affiliation:
Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, USA
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Abstract

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We define the notions of the pseudo-rotation set and rotation shadowing of pseudo-orbits for endomorphisms of the circle and for homeomorphisms of the annulus. The results include: the rotation shadowing property holds for all endomorphisms of the circle; the pseudo-rotation set equals the closure of the rotation set; the closure of the rotation set varies upper-semicontinuously.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 4 , December 1988 , pp. 509 - 521
Copyright
Copyright © Cambridge University Press 1988

References

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