  In this paper, the method of constructing the asymptotics of the fundamental
solution of the Cauchy problem for a degenerate linear parabolic equation with
small diffusion is considered. Based on the results obtained in \cite{dn}, the
study extends them over the case of a degenerate equation. As in \cite{dn}, the
main technique that allows us to switch from pseudo-differential equations to
partial differential equations is the non-oscillating WKB method. A distinctive
feature of this work is a more detailed consideration on the characteristics of
the Green's function in terms of symplectic geometry. The most significant
intermediate result is presented as a theorem on the properties of the
fundamental solution.
