Piecewise linear differential systems with an algebraic line of separation
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We study the number of limit cycles of planar piecewise linear differential systems separated by a branch of an algebraic curve. We show that for each n ∈ ℕ there exist piecewise linear differential systems separated by an algebraic curve of degree n having [n/2] hyperbolic limit cycles. Moreover, when n=2,3, we study in more detail the problem, considering a perturbation of a center and constructing examples with 4 and 5 limit cycles, respectively. These results follow by proving that the set of functions generating the first order averaged function associated to the problem is an extended complete Chebyshev system in a suitable interval.
CitationGasull, A., Torregrosa, J., & Zhang, X. (2020). Piecewise linear differential systems with an algebraic line of separation. Electronic Journal of Differential Equations, 2020(19), pp. 1-14.
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