On the Center of Continuous Maps of Dendrites |
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Authors: | LS Efremova EN Makhrova |
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Institution: | Department of Mathematics , University of Nizhny Novgorod , Nizhny Novgorod, 603950, Russia |
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Abstract: | The structure and the depth of the center of a continuous map of a dendrite with a closed countable set of branch points of a finite order are studied. It is proved that the center of that map coincides with the closure of the set of periodic points. It is shown also that for an arbitrary natural number n S 2 there are the dendrite X n with a closed countable set of branch points of a finite order and the continuous map f n : X n M X n with n as the depth of the center. |
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Keywords: | Continuous Map Dendrite Branch Point Periodic Point Center Depth Of The Center |
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