On the total disconnectedness of the quotient Aubry set
Alfonso Sorrentino
TL;DR
This paper proves that for specific Lagrangians, the quotient Aubry set is totally disconnected, and explores its connection to a Morse-Sard type property for Hamilton-Jacobi critical subsolutions.
Contribution
It establishes the total disconnectedness of the quotient Aubry set for certain Lagrangians and links this to a Morse-Sard type property in Hamilton-Jacobi theory.
Findings
Quotient Aubry set is totally disconnected for certain Lagrangians
Connection between Aubry set disconnectedness and Morse-Sard property
Insights into the structure of critical subsolutions of Hamilton-Jacobi equations
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Differential Equations and Dynamical Systems · Advanced Topics in Algebra