On the total disconnectedness of the quotient Aubry set
arXiv:0704.0129
Abstract
In this paper we show that the quotient Aubry set associated to certain Lagrangians is totally disconnected (i.e., every connected component consists of a single point). Moreover, we discuss the relation between this problem and a Morse-Sard type property for (difference of) critical subsolutions of Hamilton-Jacobi equations.
21 pages, accepted for publication in Ergodic Theory Dynam. Systems