Birkhoff Normal Forms and KAM Theory for Gumowski-Mira Equation

Abstract

By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: xn+1=(2axn)/(1+xn2)-xn-1, n=0,1,…, where x-1,x0∈(-∞,∞), and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions.