We report here the existence of Ermanno-Bernoulli type invariants for the
Manev model dynamics which may be viewed upon as remnants of Laplace-Runge-Lenz
vector whose conservation is characteristic of the Kepler model. If the orbits
are bounded these invariants exist only when a certain rationality condition is
met and thus we have superintegrability only on a subset of initial values. We
analyze real form dynamics of the Manev model and derive that it is always
superintegrable. We also discuss the symmetry algebras of the Manev model and
its real Hamiltonian form.Comment: 12 pages, LaTeX, In: Prof. G. Manev's Legacy in Contemporary
Astronomy, Theoretical and Gravitational Physics, V. Gerdjikov, M. Tsvetkov
(Eds), Heron Press, Sofia 2005, pp. 155-16
