English

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.

Keywords

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

R2 v1 2026-06-28T12:08:35.764Z