On the question of the stability of the periodic trajectories of Birkhoff's billiard (Q1117530)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the question of the stability of the periodic trajectories of Birkhoff's billiard |
scientific article; zbMATH DE number 4092406
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the question of the stability of the periodic trajectories of Birkhoff's billiard |
scientific article; zbMATH DE number 4092406 |
Statements
On the question of the stability of the periodic trajectories of Birkhoff's billiard (English)
0 references
1988
0 references
The stability of the periodic solutions of the Birkhoff billiard are investigated. A formula, connecting the stability in the first approximation of the periodic trajectory with its Morse index, is obtained. A criterion for the hyperbolicity (ellipticity) of a periodic solution of the billiard is obtained. It is proved that to a polygon of maximal length, inscribed in the billiard curve, there corresponds a hyperbolic periodic trajectory. The connection between the obtained results and the corresponding theorems regarding closed geodesics on Riemann surfaces is discussed.
0 references
stability
0 references
periodic solutions
0 references
Birkhoff billiard
0 references
Morse index
0 references
hyperbolicity
0 references
ellipticity
0 references
0.97980857
0 references
0.9352675
0 references
0.93375653
0 references
0.9331785
0 references
0.92892694
0 references
0.9212123
0 references
0.92092174
0 references
0.9192595
0 references
0.91830885
0 references
0.9169281
0 references
