01-424 Diogo A. Gomes

Viscosity Solutions of Hamilton-Jacobi Equations, and Asymptotics for Hamiltonian Systems (233K, PDF) Nov 14, 01

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Abstract. In this paper we apply the theory of viscosity solutions of Hamilton-Jacobi equations to understand the structure of certain Hamiltonian flows. In particular, we describe the asymptotic behavior of minimizing orbits, and prove analogs of the classical Hamilton-Jacobi integrability theory that hold under very general conditions. Then, combining partial differential equations techniques with dynamical systems ideas (Mather measures, ergodicity) we study solutions of time-independent Hamilton-Jacobi equation, namely, uniform continuity, difference quotients and non-uniqueness.

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