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We investigate the relations holding among generalized dimensions ofinvariant measures in dynamical systems and similar quantities defined by thescaling of global averages of powers of return times. Because of a heuristicuse of Kac theorem, these latter have been used in place of the former innumerical and experimental investigations; to mark this distinction, we callthem return time dimensions. We derive a full set of inequalities linkingmeasure and return time dimensions and we comment on their optimality with theaid of two maps due to von Neumann -- Kakutani and to Gaspard -- Wang. Weconjecture the behavior of return time dimensions in a typical system. We onlyassume ergodicity of the dynamical system under investigation.

The global statistics of return times: return time dimensions versus generalized measure dimensions