On invariants and forbidden sets
Dynamical Systems
2012-05-29 v2
Abstract
We introduce six new algebraic invariants for rational difference equations. We use these invariants to perform a reduction of order in each case. This reduction of order allows us to find forbidden sets in each case. These six cases include two linear fractional rational difference equations of order greater than one. In all six cases, we give a closed form solution for all initial conditions which are not in the forbidden set. In all six cases, the initial conditions and parameters are assumed to be arbitrary complex numbers.
Cite
@article{arxiv.1203.2170,
title = {On invariants and forbidden sets},
author = {Frank J. Palladino},
journal= {arXiv preprint arXiv:1203.2170},
year = {2012}
}
Comments
2 figures, a typo in one of the closed form solutions in the first version of the article has now been corrected