### Abstract

Original language | English |
---|---|

Pages (from-to) | 1135-1140 |

Number of pages | 6 |

Journal | Physics Letters A |

Volume | 374 |

Issue number | 9 |

Early online date | 28 Dec 2009 |

DOIs | |

Publication status | Published - 15 Feb 2010 |

### Fingerprint

### Keywords

- dynamical-systems
- metric invariant
- return times
- statistics
- complex
- plots
- automorphisms
- signals

### Cite this

*Physics Letters A*,

*374*(9), 1135-1140. https://doi.org/10.1016/j.physleta.2009.12.057

**Kolmogorov-Sinai entropy from recurrence times.** / Baptista, M. S.; Ngamga, E. J.; Pinto, Paulo R. F.; Brito, Margarida; Kurths, J.

Research output: Contribution to journal › Article

*Physics Letters A*, vol. 374, no. 9, pp. 1135-1140. https://doi.org/10.1016/j.physleta.2009.12.057

}

TY - JOUR

T1 - Kolmogorov-Sinai entropy from recurrence times

AU - Baptista, M. S.

AU - Ngamga, E. J.

AU - Pinto, Paulo R. F.

AU - Brito, Margarida

AU - Kurths, J.

PY - 2010/2/15

Y1 - 2010/2/15

N2 - 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.

AB - 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.

KW - dynamical-systems

KW - metric invariant

KW - return times

KW - statistics

KW - complex

KW - plots

KW - automorphisms

KW - signals

U2 - 10.1016/j.physleta.2009.12.057

DO - 10.1016/j.physleta.2009.12.057

M3 - Article

VL - 374

SP - 1135

EP - 1140

JO - Physics Letters A

JF - Physics Letters A

SN - 0375-9601

IS - 9

ER -