Bonatti and da Luz have introduced the class of multi-singular hyperbolic vector fields to characterize systems whose periodic orbits and singularities do not bifurcate under perturbation (called star vector fields).
In this paper, we study the Sinaï-Ruelle-Bowen measures for multi-singular hyperbolic vector fields: in a
C
1
C^1
open and
C
1
C^1
dense subset of multi-singular hyperbolic vector fields, each
C
∞
C^\infty
one admits finitely many physical measures whose basins cover a full Lebesgue measure subset of the manifold. Similar results are also obtained for
C
1
C^1
generic multi-singular hyperbolic vector fields.