On the Abstract Properties of Markov Graphs for Maps on Trees

Kozerenko, Sergiy

doi:10.37560/matbil17200022k

matbil

2017

DOI: 10.37560/matbil17200022k

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On the Abstract Properties of Markov Graphs for Maps on Trees

Sergiy Kozerenko¹

Abstract: Having a dynamical system on the vertex set of a finite tree, one can construct the corresponding Markov graph which is the digraph that encodes covering relation between edges in a tree. Representatives of isomorphism classes of Markov graphs are called M-graphs. In this paper we prove that the class of M-graphs is closed under several prescribed digraph transformations (such as deletion of a vertex in a digraph or taking the disjoint union of digraphs, for example). We also give a complete list of tournament… Show more

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2018

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“…The next theorem gives a characterization of maps which attain the lower bound from Proposition 3. 5.…”

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confidence: 99%

Linear and metric maps on trees via Markov graphs

Kozerenko¹

2018

Commentationes Mathematicae Universitatis Carolinae

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The main focus of combinatorial dynamics is put on the structure of periodic points (and the corresponding orbits) of topological dynamical systems. The first result in this area is the famous Sharkovsky's theorem which completely describes the coexistence of periods of periodic points for a continuous map from the closed unit interval to itself. One feature of this theorem is that it can be proved using digraphs of a special type (the so-called periodic graphs). In this paper we use Markov graphs (which are the natural generalization of periodic graphs in case of dynamical systems on trees) as a tool to study several classes of maps on trees. The emphasis is put on linear and metric maps.

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“…The next theorem gives a characterization of maps which attain the lower bound from Proposition 3. 5.…”

mentioning

confidence: 99%

Linear and metric maps on trees via Markov graphs

Kozerenko¹

2018

Commentationes Mathematicae Universitatis Carolinae

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show abstract

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On the Abstract Properties of Markov Graphs for Maps on Trees

Cited by 1 publication

References 8 publications

Linear and metric maps on trees via Markov graphs

Linear and metric maps on trees via Markov graphs

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