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arXiv · 2610.08725

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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Carlos Vinícius das Neves Silva, Paulo Ricardo da Silva. 2026-10-06. Bifurcation of limit cycles in piecewise holomorphic systems separated by two external circles. https://arxiv.org/abs/2610.08725

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