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Homoclinic and non-wandering points for maps of the circle

Published online by Cambridge University Press:  19 September 2008

Louis Block ,
Ethan Coven ,
Irene Mulvey  and
Zbigniew Nitecki
Louis Block
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
Ethan Coven
Affiliation:
Department of Mathematics, Wesleyan University, Middleton, CT 06457, USA
Irene Mulvey
Affiliation:
Department of Mathematics, Swarthmore College, Swarthmore, PA 19081, USA
Zbigniew Nitecki
Affiliation:
Department of Mathematics, Tufts University, Medford, MA 02155, USA
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Abstract

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For continuous maps ƒ of the circle to itself, we show: (A) the set of nonwandering points of ƒ coincides with that of ƒn for every odd n; (B) ƒ has a horseshoe if and only if it has a non-wandering homoclinic point; (C) if the set of periodic points is closed and non-empty, then every non-wandering point is periodic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 3 , Issue 4 , December 1983 , pp. 521 - 532
Copyright
Copyright © Cambridge University Press 1983

References

REFERENCES

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