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These notes describe some applications of the analysis of ordinarydifferential equations to the study of the viscous approximation ofconservation laws in one space dimension. The exposition mostly focuses on theanalysis of invariant manifolds like the center manifold and the stablemanifold. The last section addresses a more specific issue and describes apossible way of extending the notions of center and stable manifold to someclasses of singular ordinary differential equations arising in the study of theNavier-Stokes equation in one space variable.

Notes on the study of the viscous approximation of hyperbolic problems via ODE analysis