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16. 1. 2014.
Birkhoff Normal Forms and KAM Theory for Gumowski-Mira Equation
By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: x n+1 = (2ax n)/(1 + x n 2) − x n−1, n = 0,1,…, where x −1, x 0 ∈ (−∞, ∞), and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions.