5 citations · 11 across the 8 of their papers we have counts for
9 papers
Three Trichotomy Theorems
Frank J. Palladino
We study the following kth order rational difference equation assuming nonnegative parameters and nonnegative initial conditions $$x_{n}=\frac{α+\sum_{i=1}^{k}β_{i}x_{n-i}} {A+\sum…
On rational systems in the plane. I. Riccati Cases
Gabriel Lugo, Frank J. Palladino
This paper is the first in a series of papers which will address, on a case by case basis, the special cases of the following rational system in the plane, labeled system #11. $$x_…
On competitive discrete systems in the plane. I. Invariant Manifolds
Gabriel Lugo, Frank J. Palladino
Let be a competitive map on a rectangular region . The main results of this paper give conditions which guarantee the existence of an invariant…
On invariants and forbidden sets
Frank J. Palladino
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…
On a second-order rational difference equation and a rational system
Gabriel Lugo, Frank J. Palladino
We give a complete description of the qualitative behavior of the second-order rational difference equation #166. We also establish the boundedness character for the rational syste…
On projective systems of rational difference equations
Frank J. Palladino
We discuss first order systems of rational difference equations which have the property that lines through the origin are mapped into lines through the origin. We call such systems…