Antunes, André Amaral [UNESP]Carvalho, TiagoVarão, Régis2023-07-292023-07-292023-07-25Journal of Differential Equations, v. 362, p. 52-73.1090-27320022-0396http://hdl.handle.net/11449/246989Non-smooth vector fields do not have necessarily the property of uniqueness of solution passing through a point and this is responsible to enrich the behavior of the system. Even on the plane, non-smooth vector fields can be chaotic, a feature impossible for the smooth or continuous case. We propose a new approach to better understand chaos for non-smooth vector fields by using the notion of entropy of a system. We construct a metric space of all possible trajectories of a non-smooth vector field, where we define a flow inherited by the vector field and then define the topological entropy in this scenario. As a consequence, we are able to obtain some general results and give some examples of planar non-smooth vector fields with positive (finite and infinite) entropy.52-73engArtigo10.1016/j.jde.2023.02.0532-s2.0-85149850555