Counting the number of periods in one-dimensional maps with multiple critical points
type: Item
instance of: scholarly article
title: Counting the number of periods in one-dimensional maps with multiple critical points
zbMATH Open document ID: 0808.58024
DOI: 10.1016/0378-4371(94)90176-7
author: Fageng Xie
author: Bailin Hao
published in: Physica A
publication date: 1995-03-16T00:00:00Z
review text: Consider a continuous and piecewise monotonic mapping \(f\) from the interval \([0,1]\) into itself with \(m\) monotone pieces (laps). Ask about the largest number of orbits of period \(n\) that may exist for any such map. If \(m > 2\) one can also ask restricted questions: what if we prescribe or relate the behavior of two or more turning points, for example requiring that one turning point be mapped to 0. The unrestricted orbit counting problem, as well as many restricted problems, can be solved explicitly (formulas are given) in terms of the solution to one particular restricted problem, in which all minima are mapped to 0 and all maxima are mapped to the same point. For this restricted problem many methods can be applied that were originally developed for the \(m = 2\) (logistic map) problem.
Mathematics Subject Classification ID: 37E99
zbMATH DE Number: 606920
zbMATH Keywords: periods
zbMATH Keywords: one-dimensional maps
zbMATH Keywords: kneading sequence
zbMATH Keywords: bifurcations
zbMATH Keywords: Sharkovskij ordering
reviewed by: Grzegorz Świątek
MaRDI profile type: Publication
full work available at URL: 0378-4371(94)90176-7
OpenAlex ID: W2008624415
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description: scientific article; zbMATH DE number 606920