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.
|Original language||English (US)|
|Number of pages||13|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - Apr 1 2002|
ASJC Scopus subject areas
- Applied Mathematics