Periodic orbits for multivalued maps with continuous margins of intervals
Słowa kluczowe
Multivalued map, interval map, periodic orbit, period, Sharkovskiĭ's orderAbstrakt
Let $I$ be a bounded connected subset of $ \mathbb{R}$ containing more than one point, and ${\mathcal{L}}(I)$ be the family of all nonempty connected subsets of $I$. Each map from $I$ to ${\mathcal{L}}(I)$ is called a {multivalued map}. A multivalued map $F\colon I\rightarrow{\mathcal{L}}(I)$ is called a multivalued map with continuous margins if both the left endpoint and the right endpoint functions of $F$ are continuous. We show that the well-known Sharkovskiĭ theorem for interval maps also holds for every multivalued map with continuous margins $F\colon I\rightarrow{\mathcal{L}}(I)$, that is, if $F$ has an $n$-periodic orbit and $n\succ m$ (in the Sharkovskiĭ ordering), then $F$ also has an $m$-periodic orbit.Pobrania
Opublikowane
2016-08-17
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1.
MAI, Jiehua & SUN, Taixiang. Periodic orbits for multivalued maps with continuous margins of intervals. Topological Methods in Nonlinear Analysis [online]. 17 sierpień 2016, T. 48, nr 2, s. 453–464. [udostępniono 22.7.2024].
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