Geodesic
Morse Index of Approximating Periodic Solutions for the Billiard Problem. Application to Existence Results
Canadian journal of mathematics, Tome 50 (1998) no. 3, pp. 497-524

Voir la notice de l'article provenant de la source Cambridge University Press

This paper deals with periodic solutions for the billiard problem in a bounded open set of ${{\mathbb{R}}^{N}}$ which are limits of regular solutions of Lagrangian systems with a potential well. We give a precise link between the Morse index of approximate solutions (regarded as critical points of Lagrangian functionals) and the properties of the bounce trajectory to which they converge.
DOI : 10.4153/CJM-1998-027-6
Mots-clés : 34C25, 58E50 
Bolle, Philippe. Morse Index of Approximating Periodic Solutions for the Billiard Problem. Application to Existence Results. Canadian journal of mathematics, Tome 50 (1998) no. 3, pp. 497-524. doi: 10.4153/CJM-1998-027-6
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