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

Dynamical scaling for critical states: is Chalker's ansatz valid for strong fractality?