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The authors are grateful to SECyT and FCEFyN of Universidad Nacional de Cordoba, to ETSIAE of Universidad Politecnica de Madrid, and to the Spanish Ministry of Science and Innovation (Project RTI2018-094409-B-I00).

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Del Rio, EAuthor

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July 12, 2021
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Calculation of the Statistical Properties in Intermittency Using the Natural Invariant Density

Publicated to:Symmetry-Basel. 13 (6): 935- - 2021-06-01 13(6), DOI: 10.3390/sym13060935

Authors: Elaskar, Sergio; del Rio, Ezequiel; Lorenzon, Denis;

Affiliations

Consejo Nacl Invest Cient & Tecn, RA-5000 Cordoba, Argentina - Author
Univ Nacl Cordoba, FCEFyN, Dept Aeronaut, Inst Estudios Avanzados Ingn & Tecnol IDIT, RA-5000 Cordoba, Argentina - Author
Univ Nacl Cordoba, Inst Estudios Avanzados Ingn & Tecnol IDIT, RA-5000 Cordoba, Argentina - Author
Univ Politecn Madrid, ETSIAE, Dept Fis Aplicada, Madrid 28040, Spain - Author

Abstract

We use the natural invariant density of the map and the Perron-Frobenius operator to analytically evaluate the statistical properties for chaotic intermittency. This study can be understood as an improvement of the previous ones because it does not introduce assumptions about the reinjection probability density function in the laminar interval or the map density at pre-reinjection points. To validate the new theoretical equations, we study a symmetric map and a non-symmetric one. The cusp map has symmetry about x=0, but the Manneville map has no symmetry. We carry out several comparisons between the theoretical equations here presented, the M function methodology, the classical theory of intermittency, and numerical data. The new theoretical equations show more accuracy than those calculated with other techniques.

Keywords

ChaosChaotic intermittencyI intermittencyInvariant densityMapsReinjection probability densityReinjection probability density functionSystemsTransition

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Symmetry-Basel due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2021, it was in position 34/74, thus managing to position itself as a Q2 (Segundo Cuartil), in the category Multidisciplinary Sciences. Notably, the journal is positioned en el Cuartil Q2 para la agencia Scopus (SJR) en la categoría Computer Science (Miscellaneous).

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: 1.41, 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 2025-07-09, the following number of citations:

  • WoS: 1
  • Scopus: 2

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 2025-07-09:

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

    It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

    • The work has been submitted to a journal whose editorial policy allows open Open Access publication.

    Leadership analysis of institutional authors

    This work has been carried out with international collaboration, specifically with researchers from: Argentina.