  The dynamical scaling for statistics of critical multifractal eigenstates
proposed by Chalker is analytically verified for the critical random matrix
ensemble in the limit of strong multifractality controlled by the small
parameter $b\ll 1$. The power law behavior of the quantum return probability
$P_{N}(\tau)$ as a function of the matrix size $N$ or time $\tau$ is confirmed
in the limits $\tau/N\rightarrow\infty$ and $N/\tau\rightarrow\infty$,
respectively, and it is shown that the exponents characterizing these power
laws are equal to each other up to the order $b^{2}$. The corresponding
analytical expression for the fractal dimension $d_{2}$ is found.
