Remarks on the Existence of Periodic Points for Continuous Maps on Dendrites

Let be a dendrite, be a continuous map and there exist a subcontinuum such that . In the article we study the conditions of the existence of periodic points of on . We prove the existence of a fixed point on , if is a monotone map. We obtain the conditions on a subcontinuum with an uncountable set o...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2022-07, Vol.43 (7), p.1711-1719
Main Author: Makhrova, E. N.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Dendritic structure
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
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Summary:Let be a dendrite, be a continuous map and there exist a subcontinuum such that . In the article we study the conditions of the existence of periodic points of on . We prove the existence of a fixed point on , if is a monotone map. We obtain the conditions on a subcontinuum with an uncountable set of end points under which has a periodic point. In particular, we obtain the upper estimate for the period of a periodic point on , if is a finite tree.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080222100274