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Structure of dendrites admitting an existence of an arc horseshoe

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Abstract

We say that a dendrite X admits an existence of an arc horseshoe if for any continuous map f of X into itself which has a horseshoe (A,B) one can find a natural number n such that nth iteration of f has an arc horseshoe. We investigate the structure of dendrites admitting the existence of an arc horseshoe.

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Authors and Affiliations

  1. Lobachevsky State University of Nizhni Novgorod, pr. Gagarina 23, Nizhni Novgorod, 603950, Russia

    E. N. Makhrova

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  1. E. N. Makhrova
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Correspondence to E. N. Makhrova.

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Original Russian Text © E.N. Makhrova, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 8, pp. 64–74.

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Makhrova, E.N. Structure of dendrites admitting an existence of an arc horseshoe. Russ Math. 59, 52–61 (2015). https://doi.org/10.3103/S1066369X1508006X

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  • DOI: https://doi.org/10.3103/S1066369X1508006X

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