%0 Journal Article
%T Branches of forced oscillations for a class of constrained ODEs: a topological approach
%A Alessandro Calamai
%A Marco Spadini
%J Mathematics
%D 2011
%I arXiv
%X 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 $M \subseteq \mathbb{R}^m$. 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 $\mathbb{R}^m$. As further applications, we study the set of harmonic solutions to periodic semi-esplicit differential-algebraic equations.
%U http://arxiv.org/abs/1102.1562v2