RECENT DEVELOPMENTS IN DYNAMICAL SYSTEMS: THREE PERSPECTIVES | International
Journal of Bifurcation and Chaos World Scientific Search This Journal Anywhere Quick …

We give a full topological characterization of omega limit sets of continuous maps on graphs
and we show that basic sets have similar properties as in the case of the compact interval …

We show that, for monotone graph map f, all the ω-limit sets are finite whenever f has
periodic point and for monotone dendrite map, any infinite ω-limit set does not contain …

A space X is said to be almost totally disconnected if the set of its degenerate components is
dense in X. We prove that an almost totally disconnected compact metric space admits a …

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In this paper we show that any graph map without periodic points has only one minimal set.
We describe a class of graph maps without periodic points. Our main result is to give a …

Let X be a dendrite and let f: X→ X be a continuous map that has an infinite minimal set M in
X. In the article we obtain conditions on the structure of a dendrite X and the set M, under …

Let $ G $ be a group acting by homeomorphisms on a dendrite $ X $. First, we show that any
minimal set $ M $ of $ G $ is either a finite orbit or a Cantor set (resp. a finite orbit) when the …

Minimal systems are natural generalizations of periodic orbits, and they are analogues of
ergodic measures in topological dynamics. They were defined by GD Birkhoff in 1912 [Bir] …

Let D be a dendrite and f: D→ D a continuous map. Denote by E (D) and B (D) the sets of
endpoints and branch points of D, respectively. We show that if E (D) is countable, then f is …