Abstract
Abstract We study the logarithmic Hamiltonians H = ( p x 2 + p y 2 ) ∕ 2 + log ( 1 + x 2 + y 2 ∕ q 2 ) 1 ∕ 2 , which appear in the study of the galactic dynamics. We characterize all the invariant algebraic hypersurfaces and all exponential factors of the Hamiltonian system with Hamiltonian H . We prove that this Hamiltonian system is completely integrable with Darboux first integrals if and only if q = ± 1 .
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
