| Autor: |
SERGIY KOZERENKO |
| Jazyk: |
angličtina |
| Rok vydání: |
2016 |
| Předmět: |
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| Zdroj: |
Romanian Journal of Mathematics and Computer Science, Vol 6, Iss 1, Pp 16-24 (2016) |
| Druh dokumentu: |
article |
| ISSN: |
2247-689X |
| Popis: |
One feature of the famous Sharkovsky’s theorem is that it can be proved using digraphs of a special type (the so–called Markov graphs). The most general definition assigns a Markov graph to every continuous map from the topological graph to itself. We show that this definition is too broad, i.e. every finite digraph can be viewed as a Markov graph of some one–dimensional dynamical system on a tree. We therefore consider discrete analogues of Markov graphs for vertex maps on combinatorial trees and characterize all maps on trees whose discrete Markov graphs are of the following types: complete, complete bipartite, the disjoint union of cycles, with every arc being a loop. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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