Periodic perturbations of constrained motion problems on a class of implicitly defined manifolds
Classical Analysis and ODEs
2014-05-20 v3 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1304.6114,
title = {Periodic perturbations of constrained motion problems on a class of implicitly defined manifolds},
author = {Alessandro Calamai and Marco Spadini},
journal= {arXiv preprint arXiv:1304.6114},
year = {2014}
}
Comments
15 pages, 2 figures, to appear in Communications in Contemporary Mathematics. arXiv admin note: substantial text overlap with arXiv:1102.1562