On the other hand, Mather started with a specific class of area-preserving annulus mappings, the so-called monotone twist maps.
These maps appear in mechanics as Poincare maps.
In 1982, Mather succeeded to make essential progress in this field and to prove the existence of a class of closed invariant subsets which are now called Mather sets.
Birkhauser Verlag Ag Selected chapters in the calculus of variations, paperback/jurgen moser
