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Limit of the infinite horizon discounted Hamilton-Jacobi equation

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  • Motivated by the infinite horizon discounted problem, we study the convergence of solutions of the Hamilton Jacobi equation when the discount vanishes. If the Aubry set consists in a finite number of hyperbolic critical points, we give an explicit expression for the limit. Additionaly, we give a new characterization of Mañé's critical value as for wich the set of viscosity solutions is equibounded.
    Mathematics Subject Classification: Primary: 37J50, 49L25; Secondary: 70H20.


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