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Cubic Polynomial Maps with Periodic Critical Orbit, Part II: Escape Regions
Araceli Bonifant, Jan Kiwi, John Milnor
The parameter space for monic centered cubic polynomial maps with a marked critical point of period is a smooth affine algebraic curve whose genus increases rap…
Some boundedness results for systems of two rational difference equations
Gabriel Lugo, Frank J. Palladino
We study kth order systems of two rational difference equations $$x_n=\frac{α+\sum^{k}_{i=1}β_{i}x_{n-i} + \sum^{k}_{i=1}γ_{i}y_{n-i}}{A+\sum^{k}_{j=1}B_{j}x_{n-j} + \sum^{k}_{j=1}…
Global Attractivity of the Equilibrium of a Difference Equation: An Elementary Proof Assisted by Computer Algebra System
Orlando Merino
Let and be arbitrary positive numbers. It is shown that if , then all solutions to the difference equation \tag{E} x_{n+1} = \frac{p+q x_n}{1+x_{n-1}}, \quad n=0,1,2…
Global Behavior of Solutions to Two Classes of Second Order Rational Difference Equations
Sukanya Basu, Orlando Merino
For nonnegative real numbers , , , , and such that and , the difference equation \begin{equation*} x_{n+1}=\displaystyle\frac{α+βx_{n}+γx_{n-1}…