Families of 6-cycles of third order
type: Item
instance of: scholarly article
title: Families of 6-cycles of third order
DOI: 10.1007/978-3-031-51049-6_1
author: Antonio Linero Bas
author: Daniel Nieves-Roldán
publication date: 2024-10-09T00:00:00Z
review text: In this paper, the authors improve one of their previous results by showing that the only potential 6-cycle of third-order difference equations of the form \(x_{n+3}=x_i\,g\left(x_j\right)h\left(x_k\right)\), where \(i,j,k\in\{n,n+1,n+2\}\) are pairwise distinct and \(g,h\) are continuous self-maps over the real numbers, are given by the relationship \(x_{n+3}=x_n\left(x_{n+2}/x_{n+1}\right)^2\).\N\NFor the entire collection see [Zbl 1537.37005].
reviewed by: Jonathan Hoseana
Mathematics Subject Classification ID: 39A23
Mathematics Subject Classification ID: 39A22
zbMATH DE Number: 7924165
zbMATH Keywords: \(p\)-cycle
zbMATH Keywords: functional equations
zbMATH Keywords: equilibrium points
zbMATH Keywords: homeomorphism
zbMATH Keywords: monotonicity
MaRDI profile type: Publication
cites work: A self-invertibility condition for global periodicity of difference equations
cites work: On the global periodicity of some difference equations of third order
cites work: A characterization of \(k\)-cycles
cites work: Existence and uniqueness ofp-cycles of second and third order
cites work: GENERAL CYCLES OF POTENTIAL FORM
cites work: Global periodicity and complete integrability of discrete dynamical systems
cites work: Global linearization of periodic difference equations
cites work: On Periodic Rational Difference Equations of Orderk
cites work: Frieze patterns
cites work: Some periodic and non-periodic recursions
cites work: Periodic maps on \(R^7\) without fixed points
cites work: Q3110159
cites work: On the existence of 6-cycles for some families of difference equations of third order
cites work: On Globally Periodic Solutions of the Difference Equation x n + 1 = f ( x n )/ x n − 1
cites work: On periodic cycles of the Lyness equations
description: scientific article; zbMATH DE number 7924165