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T. Bountis is grateful for the hospitality of the Centro Brasileiro de Pesquisas Fisicas, at Rio de Janeiro, during March 1-April 5, 2010, where part of the work reported here was carried out. We acknowledge partial financial support by CNPq, Capes and Faperj (Brazilian Agencies) and DGU-MEC (Spanish Ministry of Education) through Project PHB2007-0095-PC.

Analysis of institutional authors

Ruiz, G.Author

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June 9, 2019
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TIME-EVOLVING STATISTICS OF CHAOTIC ORBITS OF CONSERVATIVE MAPS IN THE CONTEXT OF THE CENTRAL LIMIT THEOREM

Publicated to:International Journal Of Bifurcation And Chaos. 22 (9): 1250208- - 2012-09-01 22(9), DOI: 10.1142/S0218127412502082

Authors: Ruiz, G; Bountis, T; Tsallis, C

Affiliations

Ctr Brasileiro Pesquisas Fis, BR-22290180 Rio De Janeiro, Brazil - Author
Natl Inst Sci & Technol Complex Syst, BR-22290180 Rio De Janeiro, Brazil - Author
Santa Fe Inst, Santa Fe, NM 87501 USA - Author
Univ Patras, CRANS, GR-26500 Patras, Greece - Author
Univ Patras, Dept Math, GR-26500 Patras, Greece - Author
Univ Politecn Madrid, Dept Matemat Aplicada & Estadist, E-28040 Madrid, Spain - Author
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Abstract

We study chaotic orbits of conservative low-dimensional maps and present numerical results showing that the probability density functions (pdfs) of the sum of N iterates in the large N limit exhibit very interesting time-evolving statistics. In some cases where the chaotic layers are thin and the (positive) maximal Lyapunov exponent is small, long-lasting quasi-stationary states (QSS) are found, whose pdfs appear to converge to q-Gaussians associated with nonextensive statistical mechanics. More generally, however, as N increases, the pdfs describe a sequence of QSS that pass from a q-Gaussian to an exponential shape and ultimately tend to a true Gaussian, as orbits diffuse to larger chaotic domains and the phase space dynamics becomes more uniformly ergodic.

Keywords

Brownian-motionCentral limit theoremConservative mapsDynamical systemsDynamicsHamiltonian-systemsModelStates

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal International Journal Of Bifurcation And Chaos due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2012, it was in position , thus managing to position itself as a Q1 (Primer Cuartil), in the category Multidisciplinary. Notably, the journal is positioned above the 90th percentile.

From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 6.17, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions Jul 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-07-04, the following number of citations:

  • WoS: 19
  • Scopus: 20

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-07-04:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 8.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 9 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 1.
  • The number of mentions on the social network X (formerly Twitter): 1 (Altmetric).

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Brazil; Greece; United States of America.

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (RUIZ LOPEZ, GUIOMAR) .