  The local induction approximation (LIA) of the Biot-Savart law is often used
for numerical and analytical investigations of vortex dynamics (in particular
in the theory of superfluid turbulence). In this paper, using renormalization
group (RG) methods, some features of the LIA is considered. The exact
statistical solution of the LIA equation is presented. The problem of
"marginal" terms, appearing at the Wilson's approach to the RG-procedure, is
concerned.
