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On Cayley conditions for billiards inside ellipsoids

Autor
Ramirez, R.
Tipus d'activitat
Article en revista
Revista
Nonlinearity
Data de publicació
2014-05
Volum
27
Número
5
Pàgina inicial
1003
Pàgina final
1028
DOI
https://doi.org/10.1088/0951-7715/27/5/1003 Obrir en finestra nova
URL
http://iopscience.iop.org/0951-7715/27/5/1003/ Obrir en finestra nova
Resum
Billiard trajectories inside an ellipsoid of Rn are tangent to n-1 quadrics of the pencil of confocal quadrics determined by the ellipsoid. The quadrics associated with periodic trajectories verify certain algebraic conditions. Cayley found them for the planar case. Dragovic and Radnovic generalized them to any dimension. We rewrite the original matrix formulation of these generalized Cayley conditions as a simpler polynomial one. We find several algebraic relations between caustic parameters an...
Paraules clau
Billiard, Cayley Condition, Integrable System, Periodic Trajectory
Grup de recerca
SD - Sistemes Dinàmics de la UPC

Participants