Finite reduction and Morse index estimates for mechanical systems
Mathematical Physics
2011-05-24 v2 Dynamical Systems
math.MP
Abstract
A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover, the Hessian of the reduced function preserves all the relevant information of the original one, by Schur's complement, which spontaneously appears in this context. Finally, the results are straightforwardly extended to the case of a Dirichlet problem on a bounded domain.
Cite
@article{arxiv.1004.1133,
title = {Finite reduction and Morse index estimates for mechanical systems},
author = {Franco Cardin and Giuseppe De Marco and Alessandro Sfondrini},
journal= {arXiv preprint arXiv:1004.1133},
year = {2011}
}
Comments
13 pages; v2: minor changes, to appear in Nonlinear Differential Equations and Applications