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PreprintCC BY 4.0arXiv

Shearless and periodic attractors in the dissipative Labyrinthic map

  • Souza L. F. B.
  • Egydio de Carvalho R.
  • Viana R. L.
  • Caldas I. L
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Abstract

The Labyrinthic map is a two-dimensional area-preserving map that features a robust transport barrier known as the shearless curve. In this study, we explore a dissipative version of this map,examining how dissipation affects the shearless curve and leads to the emergence of quasi-periodic or chaotic attractors, referred to as shearless attractors. We present a route to chaos of the shearless attractor known as the Curry-Yorke route. To investigate the multi-stability of the system, we employ basin entropy and boundary basin entropy analyses to characterize diverse scenarios. Additionally, we numerically investigate the dynamic periodic structures known as "shrimps" and "Arnold tongues" by varying the parameters of the system.

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Cite

BibTeXRIS
BibTeX
@misc{f2026shearless,
  title = {{Shearless and periodic attractors in the dissipative Labyrinthic map}},
  author = {Souza L. F. B. and Egydio de Carvalho R. and Viana R. L. and Caldas I. L},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26534},
  eprint = {2610.26534},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26534},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Shearless and periodic attractors in the dissipative Labyrinthic map
AU  - Souza L. F. B.
AU  - Egydio de Carvalho R.
AU  - Viana R. L.
AU  - Caldas I. L
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26534
UR  - https://arxiv.org/abs/2610.26534
AB  - The Labyrinthic map is a two-dimensional area-preserving map that features a robust transport barrier known as the shearless curve. In this study, we explore a dissipative version of this map,examining how dissipation affects the shearless curve and leads to the emergence of quasi-periodic or chaotic attractors, referred to as shearless attractors. We present a route to chaos of the shearless attractor known as the Curry-Yorke route. To investigate the multi-stability of the system, we employ basin entropy and boundary basin entropy analyses to characterize diverse scenarios. Additionally, we numerically investigate the dynamic periodic structures known as "shrimps" and "Arnold tongues" by varying the parameters of the system.
ER  -