Periodic orbits for multivalued maps with continuous margins of intervals
Keywords
Multivalued map, interval map, periodic orbit, period, Sharkovskiĭ's orderAbstract
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.Published
2016-08-17
How to Cite
1.
MAI, Jiehua and SUN, Taixiang. Periodic orbits for multivalued maps with continuous margins of intervals. Topological Methods in Nonlinear Analysis. Online. 17 August 2016. Vol. 48, no. 2, pp. 453 - 464. [Accessed 24 April 2024].
Issue
Section
Articles
Stats
Number of views and downloads: 0
Number of citations: 0