Periodicities in Nonlinear Difference Equations

By E. Grove, G. Ladas. 2004

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On the Rational Recursive Sequence (2008, unknown): “(The linearized stability theorem; see[15,18,19]).”
Qualitative Properties for a Fourth Order Rational Difference Equation (2010, background): “Theorem B [19] Let g : [p,q]2 →[p,q] be a continuous function, where p and q are real numbers with p < q , and consider the following equation: xn+1 = g(xn, xn−1), n= 0,1, .”
Dynamics of rational difference equations containing quadratic terms (2008, background): “The following general result which involves coordinate-wise monotonicity is from [9] (but also see [8], [10], [12] or [15]).”
Dynamic behavior of a second-order nonlinearrational difference equation (2015, background): “Now we recall some definitions and results that will be useful in our investigation; for more details see [11].”
On the Dynamics of a Rational Difference Equation, Part 1 (2008, background): “(El-Metwally, Grove, Ladas, and Voulov [9] or [10]) Let I be an interval of real numbers and let f ∈ C(Ik+1, I ).”
Dynamics of the Rational Difference Equation (2014, unknown): “(ii) If be− dh 6= 0, we deduce from (9) and (11) that |ρ0|+ |ρ1|+ |ρ2|+ |ρ3| < 1, and hencẽx of Eq.”
Rational systems in the plane (2009, background): “Consider the system (21, 38): xnþ1 1⁄4 a1 þ b1xn yn ynþ1 1⁄4 g2yn A2 þ B2xn þ yn (9)>>= >>; ; n 1⁄4 0; 1; .”