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Article . 2020
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Monotone Maps on Dendrites

Monotone maps on dendrites
Authors: Makhrova, E. N.;

Monotone Maps on Dendrites

Abstract

Summary: Let \(X\) be a dendrite, \(f : X \to X\) be a monotone map. In the article the relationship between a structure of a dendrite \(X\) and dynamical properties of \(f\) is studied. Namely the relation between a structure of \(X\) and a structure of the sets of periodic points of \(f\), non-wandering points of \(f\), \(\omega\)-limit sets of trajectories is established. The structure of dendrites on which there exist monotone pointwise chain recurrent maps is characterized. The structure of dendrites on which there exist monotone maps with homoclinic points is described.

Keywords

recurrent maps, periodic points, Notions of recurrence and recurrent behavior in topological dynamical systems, Special maps on metric spaces, Topological spaces of dimension \(\leq 1\); curves, dendrites, Dynamics in general topological spaces, dendrite

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Top 10%
Average
Average
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