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

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

2011-02-08

arxiv.org/abs/1102.1562v2

Mathematics

Classical Analysis and ODEs

14 pages, final version, to appear in Nonlinear Differential Equations and Applications

Scientific paper

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.

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