Characterization of chaotic systems at transition points through dimension spectra

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.