English

Melnikov analysis for planar piecewise linear vector fields with algebraic switching curve $y^n-x^m=0$

Dynamical Systems 2022-02-08 v1 Classical Analysis and ODEs

Abstract

This paper is devoted to the study of the maximum number of limit cycles, H(m,n)H(m,n), of a planar piecewise linear differential system with two zones separated by the curve ynxm=0y^n-x^m=0, with n,mn,m being positive integers. More precisely, we provide a lower estimate of H(m,n) H(m,n). for all m,nNm,n\in \mathbb{N}, for piecewise linear perturbations of the linear center using some recent results about Chebyshev systems with positive accuracy and Melnikov Theory

Cite

@article{arxiv.2202.02846,
  title  = {Melnikov analysis for planar piecewise linear vector fields with algebraic switching curve $y^n-x^m=0$},
  author = {Cintia C. Santos and Oscar A. R. Cespedes},
  journal= {arXiv preprint arXiv:2202.02846},
  year   = {2022}
}
R2 v1 2026-06-24T09:22:49.257Z