Limit cycles and invariant cylinders for a class of continuous and discontinuous vector field in dimention 2n
Authors:
Mauricio Firmino Silva Lima
Affiliation:
a Centro de Matematica, Computação e Cognição, Universidade Federal do ABC, 09210-170, Santo Andre, S.P., Brazil b Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
Abstract:
The subject of this paper concerns with the bifurcation of limit cycles and invariant cylinders from a global center of a linear differential system in dimension 2n perturbed inside a class of continuous and discontinuous piecewise linear differential systems. Our main results show that at most one limit cycle and at most one invariant cylinder can bifurcate using the expansion of the displacement function up to first order with respect to a small parameter. This upper bound is reached. For proving these results we use the averaging theory in a form where the differentiability of the system is not needed.