The Morse index theorem for mechanical systems with reflections
Differential Geometry
2024-06-26 v2 Mathematical Physics
Classical Analysis and ODEs
Dynamical Systems
math.MP
Abstract
We prove a Morse index theorem for action functionals on paths that are allowed to reflect at a hypersurface (either in the interior or at the boundary of a manifold). Both fixed and periodic boundary conditions are treated.
Cite
@article{arxiv.2308.16162,
title = {The Morse index theorem for mechanical systems with reflections},
author = {Jared Wunsch and Mengxuan Yang and Yuzhou Zou},
journal= {arXiv preprint arXiv:2308.16162},
year = {2024}
}
Comments
v2: 31 pages, added a Morse Index Theorem for composition of paths