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- Dynamical_billiards abstract "A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflections from a boundary. When the particle hits the boundary it reflects from it without loss of speed. Billiard dynamical systems are Hamiltonian idealizations of the game of billiards, but where the region contained by the boundary can have shapes other than rectangular and even be multidimensional. Dynamical billiards may also be studied on non-Euclidean geometries; indeed, the very first studies of billiards established their ergodic motion on surfaces of constant negative curvature. The study of billiards which are kept out of a region, rather than being kept in a region, is known as outer billiard theory. The motion of the particle in the billiard is a straight line, with constant energy, between reflections with the boundary (a geodesic if the Riemannian metric of the billiard table is not flat). All reflections are specular: the angle of incidence just before the collision is equal to the angle of reflection just after the collision. The sequence of reflections is described by the billiard map that completely characterizes the motion of the particle. Billiards capture all the complexity of Hamiltonian systems, from integrability to chaotic motion, without the difficulties of integrating the equations of motion to determine its Poincaré map. Birkhoff showed that a billiard system with an elliptic table is integrable.".
- Dynamical_billiards thumbnail BunimovichStadium.svg?width=300.
- Dynamical_billiards wikiPageExternalLink 0208048.
- Dynamical_billiards wikiPageExternalLink sinai-ruelle-jsp2002.pdf.
- Dynamical_billiards wikiPageExternalLink billiards.html.
- Dynamical_billiards wikiPageExternalLink Bunimovich.html.
- Dynamical_billiards wikiPageExternalLink mod_SinaiBilliard.en.html.
- Dynamical_billiards wikiPageID "2160429".
- Dynamical_billiards wikiPageRevisionID "602737668".
- Dynamical_billiards hasPhotoCollection Dynamical_billiards.
- Dynamical_billiards title "Billiards".
- Dynamical_billiards urlname "Billiards".
- Dynamical_billiards subject Category:Dynamical_systems.
- Dynamical_billiards type Abstraction100002137.
- Dynamical_billiards type Attribute100024264.
- Dynamical_billiards type DynamicalSystem106246361.
- Dynamical_billiards type DynamicalSystems.
- Dynamical_billiards type PhaseSpace100029114.
- Dynamical_billiards type Space100028651.
- Dynamical_billiards comment "A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflections from a boundary. When the particle hits the boundary it reflects from it without loss of speed. Billiard dynamical systems are Hamiltonian idealizations of the game of billiards, but where the region contained by the boundary can have shapes other than rectangular and even be multidimensional.".
- Dynamical_billiards label "Bilhar dinâmico".
- Dynamical_billiards label "Billar dinámico".
- Dynamical_billiards label "Billard (mathématiques)".
- Dynamical_billiards label "Dynamical billiards".
- Dynamical_billiards sameAs Billar_dinámico.
- Dynamical_billiards sameAs Billard_(mathématiques).
- Dynamical_billiards sameAs Bilhar_dinâmico.
- Dynamical_billiards sameAs m.06r96t.
- Dynamical_billiards sameAs Q2903467.
- Dynamical_billiards sameAs Q2903467.
- Dynamical_billiards sameAs Dynamical_billiards.
- Dynamical_billiards wasDerivedFrom Dynamical_billiards?oldid=602737668.
- Dynamical_billiards depiction BunimovichStadium.svg.
- Dynamical_billiards isPrimaryTopicOf Dynamical_billiards.
