# Maciejewski A. Necessary conditions for super-integrabilityily, talk at Workshop on GDEq and Integrability, 11-15 Oct. 2010, Hradec nad Moravici, Czech Rep. (abstract)

We formulate the necessary conditions for the maximal super-integrability of certain family of classical potentials defined in the constant curvature two-dimensional spaces. We give examples of homogeneous potentials of degree ${\displaystyle -2}$ on Euclidean plane as well as their equivalents on sphere and the hyperbolic plane for which these necessary conditions are also sufficient. We show explicit forms of the additional first integrals which always can be chosen polynomial with respect to the momenta and which can be of an arbitrary high degree with respect to the momenta.