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PreprintCC BY 4.0HAL

Intrinsic dynamical shadowing of point vortices and finite time singularities

  • Xavier Leoncini
  • Perla El Kettani
  • Edgardo Ugalde
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Abstract

The trajectories of point vortices after a division using reverse collapse route are studied. In this setting, an unexpected peculiar phenomenon appears, corresponding to the shadowing of the vortex breakup. This occurs at least for a finite time, when the system evolves from three to five vortices after a breakup. An analytical study reveals that this observed numerical phenomenon is related to the condition of scale invariance, a condition necessary for the finite time singularity. Further simulations agree with our analytical findings and indicate that shadowing can occur with more than five vortices, and as well with higher order singularities . This phenomenon leads to question what a vortex is actually measuring, triggering speculations if this shadowing property could be generalized to other Hamiltonian systems with finite-time singularities.

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Cite

BibTeXRIS
BibTeX
@misc{leoncini2026intrinsic,
  title = {{Intrinsic dynamical shadowing of point vortices and finite time singularities}},
  author = {Xavier Leoncini and Perla El Kettani and Edgardo Ugalde},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25989},
  eprint = {2609.25989},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05741502v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Intrinsic dynamical shadowing of point vortices and finite time singularities
AU  - Xavier Leoncini
AU  - Perla El Kettani
AU  - Edgardo Ugalde
PY  - 2026
DA  - 2026/09/07
PB  - HAL
DO  - 10.48550/arxiv.2609.25989
UR  - https://hal.science/hal-05741502v1
AB  - The trajectories of point vortices after a division using reverse collapse route are studied. In this setting, an unexpected peculiar phenomenon appears, corresponding to the shadowing of the vortex breakup. This occurs at least for a finite time, when the system evolves from three to five vortices after a breakup. An analytical study reveals that this observed numerical phenomenon is related to the condition of scale invariance, a condition necessary for the finite time singularity. Further simulations agree with our analytical findings and indicate that shadowing can occur with more than five vortices, and as well with higher order singularities . This phenomenon leads to question what a vortex is actually measuring, triggering speculations if this shadowing property could be generalized to other Hamiltonian systems with finite-time singularities.
ER  -