Braga–Mello conjecture on arbitrary numbers of limit cycles

Let nNn\in\mathbb{N}. A piecewise linear system with two zones in the plane is a planar discontinuous piecewise linear differential system separated into two regions. A limit cycle is an isolated periodic orbit of the system.

Braga–Mello conjecture. Given nNn\in\mathbb{N}, there is a piecewise linear system with two zones in the plane with exactly nn limit cycles.

Braga and Mello proposed this conjecture after exhibiting examples with different numbers of limit cycles and emphasizing the role of the separation boundary. The paper's abstract states that the authors prove a result making the conjecture an immediate consequence, so the conjecture is solved.

Sources & referencesView supporting material

Primary source

Douglas Duarte Novaes and Enrique Ponce, “A simple solution to the Braga-Mello conjecture”, arXiv:1405.4435 (2014).

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