Direct and inverse consideration of the question of integrability

Details Direct and inverse consideration of the question of integrability Direct and inverse consideration of the question of integrability

May 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007padeu..19...29b&link_type=abstract

Publications of the Astronomy Department of the Eötvös University (PADEU), 2007, ISBN 963 463 557, Vol. 19. Edited by B. Érdi a

Astronomy and Astrophysics

Astronomy

Scientific paper

The question of the integrability of two-dimensional potentials V=V(x,y) is considered in the light and treated with the tools of the inverse problem of Dynamics. A new equation is proposed to replace the requirement of the vanishing of the Poisson bracket. Both the direct and the inverse problem for 2-D integrable potentials are studied on the basis of this equation. The cases of superintegrability and of conditional integrability are also discussed. Examples and applications are treated in some detail.

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