Turkish Journal of Mathematics
Abstract
We prove that there are no $6$-cycles of the form $x_{n+3}=x_i f(x_j,x_k),$ with $i,j,k\in\{n,n+1,n+2\}$ pairwise distinct, whenever $f:(0,\infty)\times (0,\infty)\rightarrow (0,\infty)$ is a continuous symmetric function, that is, $f(x,y)=f(y,x)$, for all $x,y>0$. Moreover, we obtain all the $6$-cycles of potential form and present some open questions relative to the search of $p$-cycles whenever symmetry does not hold.
DOI
10.55730/1300-0098.3480
Keywords
$p$-cycle, symmetric function, potential cycles, equilibrium point, iteration, homeomorphism
First Page
2043
Last Page
2060
Recommended Citation
BAS, A. L, & ROLDÁN, D. N (2023). On the existence of $6$-cycles for some families of difference equations of third order. Turkish Journal of Mathematics 47 (7): 2043-2060. https://doi.org/10.55730/1300-0098.3480
