Chaos and non-trivial minimal sets in discontinuous vector fields

Abstract

In this work some aspects on chaotic behavior and minimality in planar discontinuous vector fields are treated. The occurrence of non-deterministic chaos is observed and the concept of minimality and orientable minimality are introduced. We also investigated some relations between minimality and orientable minimality and observed the existence of new kinds of non-trivial minimal sets in chaotic systems. The approach is geometrical and involve the ordinary techniques of the discontinuous dynamical systems theory.