TY - UNPB
T1 - Introducing sub-Riemannian and sub-Finsler Billiards
AU - Dahinden, Lucas
AU - del Pino Gomez, A.
PY - 2020
Y1 - 2020
N2 - We define billiards in the context of sub-Finsler Geometry. We provide symplectic and variational (or rather, control theoretical) descriptions of the problem and show that they coincide. We then discuss several phenomena in this setting, including the failure of the reflection law to be well-defined at singular points of the boundary distribution, the appearance of gliding and creeping orbits, and the behavior of reflections at wavefronts. We then study some concrete tables in 3-dimensional euclidean space endowed with the standard contact structure. These can be interpreted as planar magnetic billiards, of varying magnetic strength, for which the magnetic strength may change under reflection. For each table we provide various results regarding periodic trajectories, gliding orbits, and creeping orbits.
AB - We define billiards in the context of sub-Finsler Geometry. We provide symplectic and variational (or rather, control theoretical) descriptions of the problem and show that they coincide. We then discuss several phenomena in this setting, including the failure of the reflection law to be well-defined at singular points of the boundary distribution, the appearance of gliding and creeping orbits, and the behavior of reflections at wavefronts. We then study some concrete tables in 3-dimensional euclidean space endowed with the standard contact structure. These can be interpreted as planar magnetic billiards, of varying magnetic strength, for which the magnetic strength may change under reflection. For each table we provide various results regarding periodic trajectories, gliding orbits, and creeping orbits.
U2 - 10.48550/arXiv.2011.12136
DO - 10.48550/arXiv.2011.12136
M3 - Preprint
SP - 1
EP - 38
BT - Introducing sub-Riemannian and sub-Finsler Billiards
PB - arXiv
ER -