Limit cycles and invariant cylinders for a class of continuous and discontinuous vector field in dimention \(2n\)
The paper deals with the bifurcation of limit cycles and invariant cylinders from a global center of a linear differential system in dimension \(2n\) perturbed inside the class of continuous or discontinuous piecewise linear vector fields represented by \[ \dot{x}=A_0x+\varepsilon F(x). \] The main results state the existence of at most one limit cycle and of at most one invariant cylinder. For the proof the authors use the expansion of the displacement function up to first order with respect to the small parameter and apply the averaging theory in a form that allows to avoid the differentiability of the system.
continuous piecewise linear vector field
discontinuous piecewise linear vector field
scientific article; zbMATH DE number 5931352