Kolmogorov-Sinai entropy from recurrence times |
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Authors: | MS Baptista EJ Ngamga Paulo RF Pinto Margarida Brito |
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Institution: | a Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, AB24 3UE Aberdeen, United Kingdom b Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal c Potsdam Institute for Climate Impact Research, Telegraphenberg, 14412 Potsdam, Germany |
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Abstract: | Observing how long a dynamical system takes to return to some state is one of the most simple ways to model and quantify its dynamics from data series. This work proposes two formulas to estimate the KS entropy and a lower bound of it, a sort of Shannon's entropy per unit of time, from the recurrence times of chaotic systems. One formula provides the KS entropy and is more theoretically oriented since one has to measure also the low probable very long returns. The other provides a lower bound for the KS entropy and is more experimentally oriented since one has to measure only the high probable short returns. These formulas are a consequence of the fact that the series of returns do contain the same information of the trajectory that generated it. That suggests that recurrence times might be valuable when making models of complex systems. |
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