Stochastic Fluctuations in Deterministic Systems

Antonio Politi*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish
Title of host publicationLarge Deviations in Physics
Subtitle of host publicationThe Legacy of the Law of Large Numbers
EditorsAngelo Vulpiani, Fabio Cecconi, Massimo Cencini, Andrea Puglisi, Davide Vergni
PublisherSpringer Berlin / Heidelberg
Pages243-261
Number of pages19
ISBN (Electronic)9783642542510
ISBN (Print)9783642542503
DOIs
Publication statusPublished - Apr 2014

Publication series

NameLecture Notes in Physics
PublisherSpringer Berlin Heidelberg
Volume885
ISSN (Print)0075-8450

Fingerprint

exponents
dynamical systems
chaos
inhomogeneity
trajectories
entropy
formalism
deviation

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

Politi, A. (2014). Stochastic Fluctuations in Deterministic Systems. In A. Vulpiani, F. Cecconi, M. Cencini, A. Puglisi, & D. Vergni (Eds.), 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.

Large Deviations in Physics: The Legacy of the Law of Large Numbers. ed. / Angelo Vulpiani; Fabio Cecconi; Massimo Cencini; Andrea Puglisi; Davide Vergni. Springer Berlin / Heidelberg, 2014. p. 243-261 (Lecture Notes in Physics; Vol. 885).

Research output: Chapter in Book/Report/Conference proceedingChapter

Politi, A 2014, Stochastic Fluctuations in Deterministic Systems. in A Vulpiani, F Cecconi, M Cencini, A Puglisi & D Vergni (eds), 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
Politi A. Stochastic Fluctuations in Deterministic Systems. In Vulpiani A, Cecconi F, Cencini M, Puglisi A, Vergni D, editors, Large Deviations in Physics: The Legacy of the Law of Large Numbers. Springer Berlin / Heidelberg. 2014. p. 243-261. (Lecture Notes in Physics). https://doi.org/10.1007/978-3-642-54251-0_9
Politi, Antonio. / Stochastic Fluctuations in Deterministic Systems. Large Deviations in Physics: The Legacy of the Law of Large Numbers. editor / Angelo Vulpiani ; Fabio Cecconi ; Massimo Cencini ; Andrea Puglisi ; Davide Vergni. Springer Berlin / Heidelberg, 2014. pp. 243-261 (Lecture Notes in Physics).
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