Abstract:
Assume that a continuous map f defined on a dendrite X has a horseshoe (A,B), where A and B are nonempty disjoint subcontinua in X. In this paper we obtain conditions for the structure of sets A and B under which some iteration of f has a linear horseshoe.
Citation:
E. N. Makhrova, “The existence of a linear horseshoe of continuous maps of dendrites”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 3, 40–46; Russian Math. (Iz. VUZ), 57:3 (2013), 32–37
\Bibitem{Mak13}
\by E.~N.~Makhrova
\paper The existence of a~linear horseshoe of continuous maps of dendrites
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 3
\pages 40--46
\mathnet{http://mi.mathnet.ru/ivm8781}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 3
\pages 32--37
\crossref{https://doi.org/10.3103/S1066369X13030043}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84876254665}
Linking options:
https://www.mathnet.ru/eng/ivm8781
https://www.mathnet.ru/eng/ivm/y2013/i3/p40
This publication is cited in the following 3 articles:
L. S. Efremova, E. N. Makhrova, “One-dimensional dynamical systems”, Russian Math. Surveys, 76:5 (2021), 821–881
V. A. Maksimenko, V. V. Makarov, A. A. Koronovskii, A. E. Hramov, “Analysis of the stability of states of semiconductor superlattice in the presence of tilted magnetic field”, Tech. Phys., 61:3 (2016), 317–323
E. N. Makhrova, “Structure of dendrites admitting an existence of arc horseshoe”, Russian Math. (Iz. VUZ), 59:8 (2015), 52–61
Citation in format AMSBIB
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