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PreprintarXiv licencearXiv

Bifurcation of limit cycles in piecewise holomorphic systems separated by two external circles

  • Carlos Vinícius das Neves Silva
  • Paulo Ricardo da Silva
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Abstract

This work investigates the number of limit cycles bifurcating from the periodic orbits of a linear center when it is perturbed by piecewise holomorphic systems with three zones separated by two external circles. We analyze how different geometric configurations of these zones influence the number of limit cycles. Moreover, we show the existence of at least sixteen limit cycles in fourth-degree piecewise polynomial holomorphic systems under certain configurations.

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Cite

BibTeXRIS
BibTeX
@misc{silva2026bifurcation,
  title = {{Bifurcation of limit cycles in piecewise holomorphic systems separated by two external circles}},
  author = {Carlos Vinícius das Neves Silva and Paulo Ricardo da Silva},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08725},
  eprint = {2610.08725},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08725},
}
RIS
TY  - UNPB
TI  - Bifurcation of limit cycles in piecewise holomorphic systems separated by two external circles
AU  - Carlos Vinícius das Neves Silva
AU  - Paulo Ricardo da Silva
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08725
UR  - https://arxiv.org/abs/2610.08725
AB  - This work investigates the number of limit cycles bifurcating from the periodic orbits of a linear center when it is perturbed by piecewise holomorphic systems with three zones separated by two external circles. We analyze how different geometric configurations of these zones influence the number of limit cycles. Moreover, we show the existence of at least sixteen limit cycles in fourth-degree piecewise polynomial holomorphic systems under certain configurations.
ER  -