On the total disconnectedness of the quotient Aubry set

Mathematics – Dynamical Systems

Scientific paper

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21 pages, accepted for publication in Ergodic Theory Dynam. Systems

Scientific paper

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.

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