Many results of persistence of quasi-periodic solutions(Kolmogorov, Arnold, Moser theory) can be recast in a-posteriori format. That is, given an approximate solution of an invariance equation, there is a true solution close to it. There are many applications of these a-posteriori format. Notably, one can take as approximate solutions the result...
de la Llave, Rafael (Georgia Institute of Technology)
University of Minnesota, Institute for Mathematics and its Applications.