  A strong Hamel function is a Hamel function that is the geodesic derivative
of some 0-homogeneous function. We prove that strong Hamel functions induce
dual symmetries and dynamical symmetries and provide the conditions such that
these symmetries are induced by strong Hamel functions. We show that projective
deformations by strong Hamel functions preserve the $\chi$-curvature and
analyse the relationship with some other functions (Funk and weak Funk
functions) preserving curvature tensors under projective deformations. In the
flat case, any Hamel function is a strong Hamel function.
