English

Finitude of Limit Cycles of Linear Piecewise ODEs in the Cylinder

Classical Analysis and ODEs 2026-05-08 v1

Abstract

Let x=S(t,x)x'=S(t,x) be a differential equation in the cylinder, linear piecewise in xx and with trigonometric coefficients in tt. In this paper, we provide an upper bound on the number of limit cycles in terms of the number of regions of the piecewise equation and the degree of the coefficients, that is, an analogue of Hilbert's 16th problem in this context.

Keywords

Cite

@article{arxiv.2605.05805,
  title  = {Finitude of Limit Cycles of Linear Piecewise ODEs in the Cylinder},
  author = {J. L. Bravo and R. Trinidad-Forte},
  journal= {arXiv preprint arXiv:2605.05805},
  year   = {2026}
}

Comments

26 pages