Asymptotic behavior of certain Ducci sequences
Greg Brockman, Ryan J. Zerr · The Fibonacci Quarterly · 2007
The Ducci map applied to vectors in ℝ3 is considered. It is shown that for any starting vector, the corresponding sequence of iterates either eventually becomes periodic or, if not eventually periodic, asymptotically approaches the zero vector. A precise characterization of which vectors exhibit each of these separate behaviors is given.