Branches of forced oscillations for a class of constrained ODEs: a topological approach

We apply topological methods to obtain global continuation results for harmonic solutions of some periodically perturbed ordinary differential equations on a k-dimensional differentiable manifold M subset of R-m. We assume that M is globally defined as the zero set of a smooth map and, as a first step, we determine a formula which reduces the computation of the degree of a tangent vector field on M to the Brouwer degree of a suitable map in R-m. As further applications, we study the set of harmonic solutions to periodic semi-explicit differential-algebraic equations.