Abstract
Let a be the topological graph shaped like the letter σ. We denote by 0 the unique branching point of σ, and by O and I the closures of the components of homeomorphics to the circle and the interval, respectively. A continuous map from a into itself satisfying that f has a fixed point in O, or f has a fixed point and is called a a map. These are the continuous self-maps of a whose sets of periods can be studied without the notion of rotation interval. We characterize the sets of periods of all a maps. © 1995 American Mathematical Society. © 1995 American Mathematical Society.
Original language | English |
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Pages (from-to) | 4899-4942 |
Journal | Transactions of the American Mathematical Society |
Volume | 347 |
Issue number | 12 |
DOIs | |
Publication status | Published - 1 Jan 1995 |
Keywords
- Periodic orbit
- Sarkovskii theorem
- Set of periods