An optimal lower bound for the size of periodic digraphs
Loading...
Date
2023
Authors
Kozerenko, Sergiy
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
A periodic digraph is the digraph associated with a periodic point of a continuous map from the unit interval to itself. This digraph encodes "covering" relation between minimal intervals in the corresponding orbit, which allows the application of purely combinatorial arguments in establishing results on the existence and co-existence of periods of periodic points (for example, in proving the famous Sharkovsky’s theorem). In this article, an optimal lower bound for the size of periodic digraphs is provided and thus some previous results of Pavlenko are tightened.
Description
Keywords
periodic digraph, Markov graph, Sharkovsky’s theorem, article
Citation
Kozerenko S. An optimal lower bound for the size of periodic digraphs / Sergiy Kozerenko // Discrete Mathematics Letters. - 2023. - Vol. 12. - P. 29-33. - https://doi.org/10.47443/dml.2023.015