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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2013 Number 3, Pages 40–46 (Mi ivm8781)

This article is cited in 3 papers

The existence of a linear horseshoe of continuous maps of dendrites

E. N. Makhrova

Chair of Diferential Equations and Mathematical Analysis, Nizhni Novgorod State University, N. Novgorod, Russia

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.

Keywords: dendrite, horseshoe, linear horseshoe.

UDC: 517.9

Received: 31.01.2012


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:3, 32–37

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