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

2011/02/08 by Alessandro Calamai, Calamai, Alessandro, Marco Spadini +1 · 1 citation
Mathematics · #34A09 #34C25 #34C40 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:34A09 #msc:34C25 #msc:34C40

paper · pdf · doi:10.48550/arxiv.1102.1562

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

arxiv created 2012/03/30 · arxiv updated 2012/04/02

Abstract

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 ⊆ 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-esplicit differential-algebraic equations.

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• Periodic perturbations of constrained motion problems on a class of implicitly defined manifolds

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