(Solutions of) holonomic systems of differential equations are formalized in the notion of a holonomic D-module. A D-module $M$ on a smooth complex analytic variety $X$ of dimension $n$ is holonomic if its characteristic variety is of dimension $n$. 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
See also
Masaki Kashiwara, On the holonomic systems of linear differential equations. II, Invent. Math. 49 (1978), no. 2, 121–135, doi
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.
V. Ginsburg, Characteristic varieties and vanishing cycles, Inv. Math. 84, 327–402 (1986)