Families of 6-cycles of third order (Q6616673)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Families of 6-cycles of third order |
scientific article; zbMATH DE number 7924165
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Families of 6-cycles of third order |
scientific article; zbMATH DE number 7924165 |
Statements
Families of 6-cycles of third order (English)
0 references
9 October 2024
0 references
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].
0 references
\(p\)-cycle
0 references
functional equations
0 references
equilibrium points
0 references
homeomorphism
0 references
monotonicity
0 references
