Periodic solutions of a Newtonian equation: Stability by the third approximation
A scalar differential Newtonian equation of the form (1) \(x'' = f(t,x)\) where \(f\) is periodic in time \(t\) is considered. It is known that in the neighbourhood of an elliptic periodic solution \(\Theta\) of (1) a so-called Birkhoff normal form with twist coefficients can be found. The twist coefficients depend on derivatives of \(f\) (evaluated at \(\Theta)\) up to the order \((2n - 1)\). Sufficient conditions of stability of the periodic solutions \(\Theta\) are found in the article on the basis of analysis of the values of the twist coefficients.
scientific article; zbMATH DE number 910000