Birkhoff Normal Forms and KAM Theory for Gumowski-Mira Equation

الملخص EN

By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: x n + 1 = ( 2 a x 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.