Original Articles

Approximate First Integrals of a Chaotic Hamiltonian System

Published in: Quaestiones Mathematicae
Volume 30 , issue 4 , 2007 , pages: 483–497

DOI: 10.2989/16073600709486215

Author(s): G. Ünal , C.M. Khalique , G.F. Alişverişçi

Keywords: HAMILTONIAN DYNAMICAL SYSTEMS , APPROXIMATE NOETHER SYMMETRIES , RESONANCES , NOETHER'S THEOREM , POINCARÉ SECTION

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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 ω ₁ = ω ₂. 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.

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