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

2013/04/30 by Alessandro Calamai, Marco Spadini
Mathematics · #math.CA #math.DS #msc:34C40 #msc:34A09 #msc:34C25

paper · pdf · doi:10.1142/s0219199714500278

15 pages, 2 figures, to appear in Communications in Contemporary Mathematics. arXiv admin note: substantial text overlap with arXiv:1102.1562

arxiv created 2014/05/17 · arxiv updated 2014/05/20

Abstract

We study forced oscillations on differentiable manifolds which are globally defined as the zero set of appropriate smooth maps in some Euclidean spaces. Given a T-periodic perturbative forcing field, we consider the two different scenarios of a nontrivial unperturbed force field and of perturbation of the zero field. We provide simple, degree-theoretic conditions for the existence of branches of T-periodic solutions. We apply our construction to a class of second order Differential-Algebraic Equations.

Citations

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