We study the behavior of chaotic systems at transition points (intermittency and crisis) through their dimension spectra f(α). In the transition regions the finite-statistics f(α) curves display a characteristic doubly peaked structure whose convergence to the asymptotic concave shape occurs for exceedingly large numbers of points. This slowing-down effect is studied for both the Duffing equation and the Hénon map and is used as a guideline in the interpretation of the spectra of NMR-laser experimental data sets.

• Received 9 May 1988

DOI:https://doi.org/10.1103/PhysRevA.39.434