https://doi.org/10.1140/epjs/s11734-025-01867-7
Regular Article
Isochronous islands in the two-harmonic standard map
1
Institute of Physics, University of São Paulo, 05508090, São Paulo, Brazil
2
Brazilian Center for Research in Physics, 22290-180, Rio de Janeiro, Brazil
3
Department of Physics, Federal University of Paraná, 82590-300, Curitiba, Paraná, Brazil
4
Interdisciplinary Center for Science, Technology, and Innovation, 81530-000, Curitiba, Paraná, Brazil
5
Lorena School of Engineering, University of São Paulo, 12602-810, Lorena, São Paulo, Brazil
6
Aix-Marseille Université, Marseille, France
a
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Received:
30
April
2025
Accepted:
17
August
2025
Published online:
26
August
2025
Abstract
Isochronous islands are regular solutions related to different chains of elliptic points but with the same winding number. These isochronous islands emerge in phase space as a response to multiple resonant perturbations and can be simulated using a simple discrete model called the two-harmonic standard map. We observed three types of isochronous transitions, which can be formed through saddle-node and pitchfork bifurcations.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjs/s11734-025-01867-7.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
B. B. Leal, A. M. O. de Almeida, R. L. Viana, I. L. Caldas: These authors contributed equally to this work.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
