### Abstract

The unavoidable presence of inhomogeneities in the phase space of a chaotic system induces fluctuations in the degree of stability, even when long trajectories are considered. The characterization of such fluctuations requires to go beyond average indicators: this is achieved with the help of the multifractal formalism which contributes to: (i) establishing a general connection between the positive Lyapunov exponents and the Kolmogorov-Sinai entropy; (ii) identifying and quantifying deviations from a purely hyperbolic dynamics; (iii) characterizing anomalous bifurcations, where the attractor looses progressively its stability. In the context of spatially extended dynamical systems, the study of Lyapunov exponent fluctuations leads to a non conventional assessment of the extensivity of the resulting dynamics. Finally, a careful study of the fluctuations allows clarifying the odd phenomenon of “stable chaos”, where an irregular dynamics is accompanied by a negative (average) Lyapunov exponent.

Original language | English |
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Title of host publication | Large Deviations in Physics |

Subtitle of host publication | The Legacy of the Law of Large Numbers |

Editors | Angelo Vulpiani, Fabio Cecconi, Massimo Cencini, Andrea Puglisi, Davide Vergni |

Publisher | Springer Berlin / Heidelberg |

Pages | 243-261 |

Number of pages | 19 |

ISBN (Electronic) | 9783642542510 |

ISBN (Print) | 9783642542503 |

DOIs | |

Publication status | Published - Apr 2014 |

### Publication series

Name | Lecture Notes in Physics |
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Publisher | Springer Berlin Heidelberg |

Volume | 885 |

ISSN (Print) | 0075-8450 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Large Deviations in Physics: The Legacy of the Law of Large Numbers*(pp. 243-261). (Lecture Notes in Physics; Vol. 885). Springer Berlin / Heidelberg. https://doi.org/10.1007/978-3-642-54251-0_9

**Stochastic Fluctuations in Deterministic Systems.** / Politi, Antonio.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Large Deviations in Physics: The Legacy of the Law of Large Numbers.*Lecture Notes in Physics, vol. 885, Springer Berlin / Heidelberg, pp. 243-261. https://doi.org/10.1007/978-3-642-54251-0_9

}

TY - CHAP

T1 - Stochastic Fluctuations in Deterministic Systems

AU - Politi, Antonio

PY - 2014/4

Y1 - 2014/4

N2 - The unavoidable presence of inhomogeneities in the phase space of a chaotic system induces fluctuations in the degree of stability, even when long trajectories are considered. The characterization of such fluctuations requires to go beyond average indicators: this is achieved with the help of the multifractal formalism which contributes to: (i) establishing a general connection between the positive Lyapunov exponents and the Kolmogorov-Sinai entropy; (ii) identifying and quantifying deviations from a purely hyperbolic dynamics; (iii) characterizing anomalous bifurcations, where the attractor looses progressively its stability. In the context of spatially extended dynamical systems, the study of Lyapunov exponent fluctuations leads to a non conventional assessment of the extensivity of the resulting dynamics. Finally, a careful study of the fluctuations allows clarifying the odd phenomenon of “stable chaos”, where an irregular dynamics is accompanied by a negative (average) Lyapunov exponent.

AB - The unavoidable presence of inhomogeneities in the phase space of a chaotic system induces fluctuations in the degree of stability, even when long trajectories are considered. The characterization of such fluctuations requires to go beyond average indicators: this is achieved with the help of the multifractal formalism which contributes to: (i) establishing a general connection between the positive Lyapunov exponents and the Kolmogorov-Sinai entropy; (ii) identifying and quantifying deviations from a purely hyperbolic dynamics; (iii) characterizing anomalous bifurcations, where the attractor looses progressively its stability. In the context of spatially extended dynamical systems, the study of Lyapunov exponent fluctuations leads to a non conventional assessment of the extensivity of the resulting dynamics. Finally, a careful study of the fluctuations allows clarifying the odd phenomenon of “stable chaos”, where an irregular dynamics is accompanied by a negative (average) Lyapunov exponent.

UR - http://www.scopus.com/inward/record.url?scp=84926611041&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-54251-0_9

DO - 10.1007/978-3-642-54251-0_9

M3 - Chapter

SN - 9783642542503

T3 - Lecture Notes in Physics

SP - 243

EP - 261

BT - Large Deviations in Physics

A2 - Vulpiani, Angelo

A2 - Cecconi, Fabio

A2 - Cencini, Massimo

A2 - Puglisi, Andrea

A2 - Vergni, Davide

PB - Springer Berlin / Heidelberg

ER -