On the total disconnectedness of the quotient Aubry set
Abstract
Description
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
21 pages, accepted for publication in Ergodic Theory Dynam. Systems