Year: 2026
Type: preprint
Abstract: We study grazing closed trajectories of the billiard flow $φ^t$ on a compact surface $(Σ,g)$ with concave boundary. Under a non-degeneracy condition, which is satisfied for example when $(Σ,g)$ has negative sectional curvature, we compute the trace of a regularized pullback $E_ε(φ^t)^* E_ε$ near a closed trajectory grazing once, which is an analogue of the Atiyah--Bott--Guillemin trace formula for closed billiard trajectories.
Source: arXiv (Cornell University)
Author: Kangabire, Alain
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214053430