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The paper mainly deals with the topological entropy of induced maps. We show that under some nonrecurrence assumption the induced map is always topologically chaotic, that is, it has positive topological entropy.Additionally we characterize topological weak and strong mixing of f in terms of the omega limit set of induced map. This allows the description of the dynamics of the map induced by a transitive graph map f on the space of all subcontinua of a given graph G. It follows that in this case has the same topological entropy as f.
Additionally we characterize topological weak and strong mixing of f in terms of the omega limit set of induced map. This allows the description of the dynamics of the map induced by a transitive graph map f on the space of all subcontinua of a given graph G. It follows that in this case has the same topological entropy as f.
