Another Billiard Problem
Let be a Riemannian manifold, a domain with boundary , and a smooth function such that , , and . We study the geodesic flow of the metric . The -distance from any point of to is finite, hence, the geodesic flow is incomplete. Regularization of the flow in a neighborhood of establishes a natural refl...
Gespeichert in:
| Veröffentlicht in: | Russian journal of mathematical physics 2024-03, Vol.31 (1), p.50-59 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | Let
be a Riemannian manifold,
a domain with boundary
, and
a smooth function such that
,
, and
. We study the geodesic flow of the metric
. The
-distance from any point of
to
is finite, hence, the geodesic flow is incomplete. Regularization of the flow in a neighborhood of
establishes a natural reflection law from
. This leads to a certain (not quite standard) billiard problem in
.
DOI
10.1134/S106192084010047 |
|---|---|
| ISSN: | 1061-9208 1555-6638 |
| DOI: | 10.1134/S106192084010047 |