%0 Journal Article %1 keyhere %A Abel, M. %A Biferale, L. %A Cencini, M. %A Falcioni, M. %A Vergni, D. %A Vulpiani, A. %D 2000 %J Physica D: Nonlinear Phenomena %K Coding Entropy Multifractals Turbulence cencini exit-time fsle theory %N 1-2 %P 12--35 %T Exit-times and epsilon-entropy for dynamical systems, stochastic processes, and turbulence %U http://www.sciencedirect.com/science/article/B6TVK-41F63R0-S/2/13e1cdee44875062f08b57a095662677 %V 147 %X We present an investigation of epsilon-entropy, h(epsilon), in dynamical systems, stochastic processes and turbulence. This tool allows for a suitable characterization of dynamical behaviours arising in systems with many different scales of motion. Particular emphasis is put on a recently proposed approach to the calculation of the epsilon-entropy based on the exit-time statistics. The advantages of this method are demonstrated in examples of deterministic diffusive maps, intermittent maps, stochastic self- and multi-affine signals and experimental turbulent data. Concerning turbulence, the multifractal formalism applied to the exit-time statistics allows us to predict that h(epsilon)~epsilon-3 for velocity-time measurement. This power law is independent of the presence of intermittency and has been confirmed by the experimental data analysis. Moreover, we show that the epsilon-entropy density of a three-dimensional velocity field is affected by the correlations induced by the sweeping of large scales.

@article{keyhere, abstract = {We present an investigation of [epsilon]-entropy, h([epsilon]), in dynamical systems, stochastic processes and turbulence. This tool allows for a suitable characterization of dynamical behaviours arising in systems with many different scales of motion. Particular emphasis is put on a recently proposed approach to the calculation of the [epsilon]-entropy based on the exit-time statistics. The advantages of this method are demonstrated in examples of deterministic diffusive maps, intermittent maps, stochastic self- and multi-affine signals and experimental turbulent data. Concerning turbulence, the multifractal formalism applied to the exit-time statistics allows us to predict that h([epsilon])~[epsilon]-3 for velocity-time measurement. This power law is independent of the presence of intermittency and has been confirmed by the experimental data analysis. Moreover, we show that the [epsilon]-entropy density of a three-dimensional velocity field is affected by the correlations induced by the sweeping of large scales.}, added-at = {2007-10-05T01:51:16.000+0200}, author = {Abel, M. and Biferale, L. and Cencini, M. and Falcioni, M. and Vergni, D. and Vulpiani, A.}, biburl = {https://www.bibsonomy.org/bibtex/21bf69cf675acbfb336caf1a826ca3076/mcencini}, description = {ScienceDirect - Physica D: Nonlinear Phenomena : Exit-times and ε-entropy for dynamical systems, stochastic processes, and turbulence}, interhash = {6f79ba185b5a63e911bcd3e3938b8f89}, intrahash = {1bf69cf675acbfb336caf1a826ca3076}, journal = {Physica D: Nonlinear Phenomena}, keywords = {Coding Entropy Multifractals Turbulence cencini exit-time fsle theory}, month = {#dec#}, number = {1-2}, pages = {12--35}, timestamp = {2007-10-05T01:51:16.000+0200}, title = {Exit-times and [epsilon]-entropy for dynamical systems, stochastic processes, and turbulence}, url = {http://www.sciencedirect.com/science/article/B6TVK-41F63R0-S/2/13e1cdee44875062f08b57a095662677}, volume = 147, year = 2000 }