### Abstract

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

Pages (from-to) | 863 -875 |

Number of pages | 14 |

Journal | Communications in Nonlinear Science & Numerical Simulation |

Volume | 16 |

Issue number | 2 |

Early online date | 25 May 2010 |

DOIs | |

Publication status | Published - Feb 2011 |

### Fingerprint

### Keywords

- Time returns
- Periodic orbits
- Lyapunov exponents
- Kolmogorov entropy

### Cite this

**Density of first Poincaré returns, periodic orbits, and Kolmogorov–Sinai entropy.** / Baptista, Murilo Da Silva.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Density of first Poincaré returns, periodic orbits, and Kolmogorov–Sinai entropy

AU - Baptista, Murilo Da Silva

PY - 2011/2

Y1 - 2011/2

N2 - It is known that unstable periodic orbits of a given map give information about the natural measure of a chaotic attractor. In this work we show how these orbits can be used to calculate the density function of the first Poincaré returns. The close relation between periodic orbits and the Poincaré returns allows for estimates of relevant quantities in dynamical systems, as the Kolmogorov–Sinai entropy, in terms of this density function. Since return times can be trivially observed and measured, our approach to calculate this entropy is highly oriented to the treatment of experimental systems. We also develop a method for the numerical computation of unstable periodic orbits.

AB - It is known that unstable periodic orbits of a given map give information about the natural measure of a chaotic attractor. In this work we show how these orbits can be used to calculate the density function of the first Poincaré returns. The close relation between periodic orbits and the Poincaré returns allows for estimates of relevant quantities in dynamical systems, as the Kolmogorov–Sinai entropy, in terms of this density function. Since return times can be trivially observed and measured, our approach to calculate this entropy is highly oriented to the treatment of experimental systems. We also develop a method for the numerical computation of unstable periodic orbits.

KW - Time returns

KW - Periodic orbits

KW - Lyapunov exponents

KW - Kolmogorov entropy

U2 - 10.1016/j.cnsns.2010.05.018

DO - 10.1016/j.cnsns.2010.05.018

M3 - Article

VL - 16

SP - 863

EP - 875

JO - Communications in Nonlinear Science & Numerical Simulation

JF - Communications in Nonlinear Science & Numerical Simulation

SN - 1007-5704

IS - 2

ER -