Periodic orbits of maps of 𝑌

Alsedà, Lluís; Llibre, Jaume; Misiurewicz, Michał

doi:10.1090/S0002-9947-1989-0958882-0

Periodic orbits of maps of $Y$
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by Lluís Alsedà, Jaume Llibre and Michał Misiurewicz PDF

Trans. Amer. Math. Soc. 313 (1989), 475-538 Request permission

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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