Approximate first integrals of a chaotic Hamiltonian system

Abstract

Approximate first integrals (conserved quantities) of a Hamiltonian dynamical system with two-degrees of freedom which arises in the modeling of galaxy have been obtained based on the approximate Noether symmetries for the resonance ω1 = ω2. Furthermore, Kolmogorov-Arnold-Moser (KAM) curves have been obtained analytically and they have been compared with the numerical ones on the Poincaré surface of section.

Quaestiones Mathematicae 30(2007), 483–497.