Abstract
Let \(X\) be a dendrite, \(f:X\to X\) be a continuous map and there exist a subcontinuum \(Y\subset X\) such that \(Y\subset f(Y)\). In the article we study the conditions of the existence of periodic points of \(f\) on \(Y\). We prove the existence of a fixed point on \(Y\), if \(f\) is a monotone map. We obtain the conditions on a subcontinuum \(Y\) with an uncountable set of end points under which \(Y\) has a periodic point. In particular, we obtain the upper estimate for the period of a periodic point on \(Y\), if \(Y\) is a finite tree.
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Makhrova, E.N. Remarks on the Existence of Periodic Points for Continuous Maps on Dendrites. Lobachevskii J Math 43, 1711–1719 (2022). https://doi.org/10.1134/S1995080222100274
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DOI: https://doi.org/10.1134/S1995080222100274