
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.
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
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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