Trees with snowflakes and zero entropy maps
type: Item
instance of: scholarly article
title: Trees with snowflakes and zero entropy maps
zbMATH Open document ID: 0804.54021
DOI: 10.1016/0040-9383(94)90019-1
published in: Topology
publication date: 1995-01-19T00:00:00Z
review text: A one-dimensional connected and contractible branching manifold with finitely many branching points is called a tree, and a finite union of trees is called a forest. The main result of the paper is theorem 3, which gives necessary and sufficient conditions that a continuous self- mapping of a forest has zero entropy. This generalizes the corresponding statement for maps of the interval based on Sharkovskij's theorem [\textit{A. N. Sharkovskij}, Ukr. Mat. J. 16, 61-71 (1964; Zbl 0122.175)] on the structure of periodic points and on Misiurewicz's theorem [\textit{M. Misiurewicz}, Bull. Pol. Acad. Sci., Sér. Sci. Math. 27, 167-169 (1979; Zbl 0423.54032)] on the existence of horseshoes for positive entropy maps.
reviewed by: Manfred Denker
Mathematics Subject Classification ID: 54C70
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 37E99
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 590282
zbMATH Keywords: one-dimensional map
zbMATH Keywords: Sharkovskij's theorem
author: Alexander Blokh
MaRDI profile type: Publication
full work available at URL: 0040-9383(94)90019-1
OpenAlex ID: W2149432366
Wikidata QID: Q127677545
description: scientific article; zbMATH DE number 590282