Abstract
Our main concern is to discuss the existence of periodic orbits for certain piecewise linear differential systems in \(\mathbb {R}^ n\), where the discontinuity set is a hypersurface \(\Sigma .\) Using the fact that every linear differential system is always completely integrable, we illustrate for two piecewise linear differential systems, one in \(\mathbb {R}^3\) and the other in \(\mathbb {R}^4\), how to study analytically their periodic solutions.
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