Dispersive kinetics. A host of challenges for chaotic dynamics

The specific reaction rate k(t) similar to t(<(alpha)over cap> - 1), 0 < <( alpha)over cap> less than or equal to 1, is used in numerous areas of conde nsed phase chemistry to account for the dispersion of reactant reactivity s een at time scales shorter than or comparable to the time scale of structur al relaxations of systems. So far, the use of Ic(t), which introduces the f ractal-time into the chemical kinetics, was rationalized by random-walk mod eling, incorporating the long-tailed (Levy) distribution Psi(t) similar to t(- <(alpha)over cap> - 1) of times between the events that limit the motio n of reactants. Now, new perspectives for developments in kinetics are seen as the once abstract notion of fractal space and time now appear naturally and are inevitable in chaotic dynamical systems.