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This work has been financially supported by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe" (Grant No. PID2019-105554GB-I00) .

Analysis of institutional authors

Nieto, Alexandre RAuthorSeoane, Jesus MAuthorSanjuán M.a.f.Author

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Period-doubling bifurcations and islets of stability in two-degree-of-freedom Hamiltonian systems

Publicated to:Physical Review e. 107 (5): 54215- - 2023-05-18 107(5), DOI: 10.1103/physreve.107.054215

Authors: Nieto, Alexandre R; Seoane, Jesus M; Sanjuan, Miguel A F

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Abstract

In this paper, we show that the destruction of the main Kolmogorov-Arnold-Moser (KAM) islands in two -degree-of-freedom Hamiltonian systems occurs through a cascade of period-doubling bifurcations. We calculate the corresponding Feigenbaum constant and the accumulation point of the period-doubling sequence. By means of a systematic grid search on exit basin diagrams, we find the existence of numerous very small KAM islands ("islets") for values below and above the aforementioned accumulation point. We study the bifurcations involving the formation of islets and we classify them in three different types. Finally, we show that the same types of islets appear in generic two-degree-of-freedom Hamiltonian systems and in area-preserving maps.

Keywords

Accumulation pointsArea-preserving mapsBifurcation (mathematics)Computational complexityComputer simulationDegrees of freedom (mechanics)Feigenbaum constantsGeneric two-degree of freedomsGrid searchHamiltonian systemsHamiltoniansKolmogorovNonlinear dynamicsNonlinear systemPeriod doubling bifurcationPeriod doubling sequenceTwo-degree-of-freedom

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Physical Review e 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, 2023, it was in position 12/60, thus managing to position itself as a Q1 (Primer Cuartil), in the category Physics, Mathematical.

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: 4.59, 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 May 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-05-29, the following number of citations:

  • WoS: 2
  • Scopus: 2
  • OpenCitations: 1

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 2025-05-29:

  • 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: 3.
  • 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: 4 (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: 2.95.
  • The number of mentions on the social network X (formerly Twitter): 5 (Altmetric).

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: Lithuania.

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 (Rodríguez Nieto, Alexandre) and Last Author (Fernández Sanjuán, Miguel Ángel).