 Initial conditions for are redefined as
Equations are easily integrated; the solution that satisfies the condition is
where "b"0 and "c"0 are two more constants.It can easily be seen that the asymptotic of functions at "t" → 0 is .The asymptotic expressions of these functions and the function "t"(τ) at τ → −∞ is

Expressing "a", "b", "c" as functions of "t", one has
where
Then
The above shows that perturbation acts in such a way that it changes one Kasner mode with another Kasner mode, and in this process the negative power of "t" flips from direction l to direction m