Analogue ensembles in Takens-reconstructed phase spaces have volumes and time-dispersion dynamics determined by the scale-invariance properties of the underlying stochastic process.
Mantica, The global statistics of return times: return time dimensions versus generalized measure dimensions, Journal of statistical Physics 138 (2010) 701–727
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Structural and Lagrangian properties of analogue ensembles to characterize multifractality of stochastic processes
Analogue ensembles in Takens-reconstructed phase spaces have volumes and time-dispersion dynamics determined by the scale-invariance properties of the underlying stochastic process.