Bifurcation of limit cycles from an nn-dimensional linear center inside a class of piecewise linear differential systems

Let nn be an even integer. We study the bifurcation of limit cycles from the periodic orbits of the nn-dimensional linear center given by the differential system ẋ1=−x2,ẋ2=x1,…,ẋn−1=−xn,ẋn=xn−1, perturbed inside a class of piecewise linear differential systems. Our main result shows that at most (4n−6)n/2−1(4n−6)n/2−1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result we use the averaging theory in a form where the differentiability of the system is not needed.