Computer analysis of periodic orbits of discontinuous vector fields (Q1404421)

The authors consider a class of discontinuous vector fields on four-dimensional Euclidean space, which present discontinuities at a submanifold of codimension one. Using methods of computer algebra some exact results are derived, concerning the existence of families of periodic orbits with various symmetry properties. Some of the methods used (Gröbner bases, analysis of semi-algebraic varieties) are novel in this area on nonlinear dynamics, which is relevant to engineering applications.