Polynomial entropy for interval maps and lap number
type: Item
instance of: scholarly article
title: Polynomial entropy for interval maps and lap number
zbMATH Open document ID: 1468.37038
author: José Barbosa Gomes
author: Mário Jorge Dias Carneiro
published in: Qualitative Theory of Dynamical Systems
publication date: 2021-05-07T00:00:00Z
review text: The concept of polynomial entropy was introduced by \textit{J.-P. Marco} [Regul. Chaotic Dyn. 18, No. 6, 623--655 (2013; Zbl 1286.70022)]. Here the authors obtain two upper bounds on the polynomial entropy for piecewise monotone interval maps using the number of monotone pieces of iterates of the maps (lap number) and the total variation of the iterates. The authors also present a lower bound for the polynomial entropy which holds if the preimages of the set of turning points does not accumulate on the set of turning points.
Mathematics Subject Classification ID: 37E05
Mathematics Subject Classification ID: 37B40
zbMATH DE Number: 7345484
zbMATH Keywords: entropy
zbMATH Keywords: polynomial entropy
zbMATH Keywords: interval maps
zbMATH Keywords: quadratic family
zbMATH Keywords: lap number
reviewed by: Steve Pederson
MaRDI profile type: Publication
full work available at URL: s12346-021-00456-y
OpenAlex ID: W3135481687
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DOI: 10.1007/S12346-021-00456-Y
description: scientific article; zbMATH DE number 7345484