  According to Pixton, there are Morse-Smale diffeomorphisms of the 3-sphere
which have no energy function, that is a Lyapunov function whose critical
points are all periodic points of the diffeomorphism. We introduce the concept
of quasi-energy function for a Morse-Smale diffeomorphism as a Lyapunov
function with the least number of critical points and construct a quasi-energy
function for any diffeomorphism from some class of Morse-Smale diffeomorphisms
on the 3-sphere.
