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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Periodic orbits of maps of $ Y$


Authors: Lluís Alsedà, Jaume Llibre and Michał Misiurewicz
Journal: Trans. Amer. Math. Soc. 313 (1989), 475-538
MSC: Primary 58F20; Secondary 54H20
MathSciNet review: 958882
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Abstract: We introduce some notions that are useful for studying the behavior of periodic orbits of maps of one-dimensional spaces. We use them to characterize the set of periods of periodic orbits for continuous maps of $ Y = \{ z \in {\mathbf{C}}:{z^3} \in [0,1]\} $ into itself having zero as a fixed point. We also obtain new proofs of some known results for maps of an interval into itself.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0958882-0
PII: S 0002-9947(1989)0958882-0
Keywords: Periodic orbit, primary orbit, set of periods, Šarkovskiĭ theorem
Article copyright: © Copyright 1989 American Mathematical Society