BA6183, 40 St. George Street

Abstract:  In the study of the existence of diffusing orbits for Lagrangian dynamical systems, an important role/obstruction is played by the so-called quotient Aubry set. An interesting question is: under which hypotheses is this set totally disconnected? We will show that this problem can be, quite surprisingly, related to a Sard-like property for certain subsolutions of Hamilton-Jacobi equation. Then, we will use this relation to prove total disconnectedness, under suitable conditions on the Lagrangian.