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 ∈ C: z3 ∈ [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. © 1989 American Mathematical Society.
Original language | English |
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Pages (from-to) | 475-538 |
Journal | Transactions of the American Mathematical Society |
Volume | 313 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jan 1989 |
Keywords
- Periodic orbit
- Primary orbit
- Set of periods
- Šarkovskii theorem