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| By a result of Blokh from 1984, every transitive map $f:X\to X$ of a tree $X$ has the relative specification property. That is, there is a regular periodic decomposition $(D_0,\dots,D_{m-1})$ of $X$ such that the restrictions $f^m|_{D_i}:D_i\to D_i$ have the specification property. This is not true for transitive dendrite maps, as was shown by Hoehn and Mouron. They constructed a weakly mixing dendrite map which is not mixing. Recently, we gave another example showing that Blokh's theorem cannot be extended to dendrites; we constructed a transitive map of a dendrite with infinite decomposition ideal. In the talk we review these results and we consider some of the related questions. |
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