English

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