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This work was supported by the Spanish Ministry of Economy and Competitiveness under Project No. FIS2013-40653-P and by the Spanish State Research Agency (AEI) and the European Regional Development Fund (FEDER) under Project No. FIS2016-76883-P. M.A.F.S. acknowledges the jointly sponsored financial support by the Fulbright Program and the Spanish Ministry of Education (Program No. FMECD-ST-2016).

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Nieto, ArCorresponding AuthorSeoane, JmAuthorSanjuan, MafAuthor

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Resonant behavior and unpredictability in forced chaotic scattering

Publicated to:Physical Review e. 98 (6): 62206- - 2018-12-10 98(6), DOI: 10.1103/PhysRevE.98.062206

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

Affiliations

Univ Maryland, Inst Phys Sci & Technol, College Pk, MD 20742 USA - Author
Univ Nacl Educ Distancia, Fac Ciencias, Dept Fis Fundamental, Paseo Senda Rey 9, E-28040 Madrid, Spain - Author
Univ Rey Juan Carlos, Dept Fis, Nonlinear Dynam Chaos & Complex Syst Grp, Tulipan S-N, Madrid 28933, Spain - Author

Abstract

Chaotic scattering in open Hamiltonian systems is a topic of fundamental interest in physics, which has been mainly studied in the purely conservative case. However, the effect of weak perturbations in this kind of system has been an important focus of interest in the past decade. In a previous work, the authors studied the effects of a periodic forcing in the decay law of the survival probability, and they characterized the global properties of escape dynamics. In the present paper, we add two important issues in the effects of periodic forcing: the fractal dimension of the set of singularities in the scattering function and the unpredictability of the exit basins, which is estimated by using the concept of basin entropy. Both the fractal dimension and the basin entropy exhibit a resonant-like decrease as the forcing frequency increases. We provide a theoretical reasoning which could justify this decreasing in the fractality near the main resonant frequency that appears for omega approximate to 1. We attribute the decrease in the basin entropy to the reduction of the area occupied by the Kolmogorov-Arnold-Moser (KAM) islands and the basin boundaries when the frequency is close to the resonance. On the other hand, the decay rate of the exponential decay law shows a minimum value of the amplitude, A(c), which reflects the complete destruction of the KAM islands in the resonance. Finally, we have found the existence of Wada basins for a wide range of values of the frequency and the forcing amplitude. We expect that this work could be potentially useful in research fields related to chaotic Hamiltonian pumps and oscillations in chemical reactions and companion galaxies, among others.

Keywords

BasinsChaotic scatteringDecay (organic)EntropyEscapesExponential decaysForcing amplitudesForcing frequenciesFractal dimensionFractal structuresHamiltonian systemsHamiltoniansNatural frequenciesScattering functionsSurvival probabilitiesWeak perturbation

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, 2018, it was in position 7/55, 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: 4.13, 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 Jun 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-18, the following number of citations:

  • WoS: 9
  • Scopus: 9
  • OpenCitations: 9

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 2025-06-18:

  • 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: 4.
  • 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: 1.85.
  • The number of mentions on the social network X (formerly Twitter): 4 (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: 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 (Rodríguez Nieto, Alexandre) and Last Author (Fernández Sanjuán, Miguel Ángel).

the author responsible for correspondence tasks has been Rodríguez Nieto, Alexandre.