Theory and Modern Applications
From: The roles of conic sections and elliptic curves in the global dynamics of a class of planar systems of rational difference equations
Number of terms in the denominator of T i ( x n , y n ), i = 1,2
Formula for the denominator of T i ( x n , y n ), i = 1,2
Formula for T i ( x n , y n ), i = 1,2, for which system (1) is bounded
1.
Three
A i + B i x n + C i y n
α i A i + B i x n + C i y n , β i x n A i + B i x n + C i y n , γ i y n A i + B i x n + C i y n , α i + β i x n A i + B i x n + C i y n , α i + γ i y n A i + B i x n + C i y n , β i x n + γ i y n A i + B i x n + C i y n , α i + β i x n + γ i y n A i + B i x n + C i y n
2.
Two
B i x n + C i y n
β i x n + γ i y n B i x n + C i y n , β i x n B i x n + C i y n , γ i y n B i x n + C i y n
A i + B i x n
α i A i + B i x n , β i x n A i + B i x n , α i + β i x n A i + B i x n
A i + C i y n
α i A i + C i y n , γ i y n A i + C i y n , α i + γ i y n A i + C i y n
3.
One
A i
α i / A i
B i x n
β i / B i
C i y n
γ i / C i