(Solutions of) holonomic systems of differential equations are formalized in the notion of a holonomic D-module. A D-module on a smooth complex analytic variety of dimension is holonomic if its characteristic variety is of dimension . It follows that the characteristic variety of a holonomic D-module is conic and lagrangian.
Holonomicity of D-modules is important also in geometric representation theory.
Lecture notes include
Bernard Malgrange, On irregular holonomic D-modules, Séminaires et Congrès 8, 2004, p. 391–410, pdf; Équations différentielles à coefficients polynomiaux, Progress in Math. 96, Birkhäuser 1991. vi+232 pp.
P. Maisonobe, C. Sabbah, D-modules cohérents et holonomes, Hermann, Paris 1993.