On the total disconnectedness of the quotient Aubry set
classification
🧮 math.DS
math-phmath.APmath.MP
keywords
aubryquotientassociatedcertaincomponentconnectedconsistscritical
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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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