Dynamical billiards
A dynamical billiard is a dynamical system in which a particle alternates between free motion (typically as a straight line) and specular reflections from a boundary. When the particle hits the boundary it reflects from it without loss of speed (i.e. elastic collisions). Billiards 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 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.
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Dynamical billiards
A dynamical billiard is a dynamical system in which a particle alternates between free motion (typically as a straight line) and specular reflections from a boundary. When the particle hits the boundary it reflects from it without loss of speed (i.e. elastic collisions). Billiards 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 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.
has abstract
A dynamical billiard is a dyna ...... elliptic table is integrable.
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Dynamisches Billard wird ein d ...... r nächsten Reflexion abbildet.
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Um bilhar dinâmico é um sistem ...... esloca ao largo de geodésicas.
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Un billar dinámico es un siste ...... ientes de su espacio de fases.
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Un billard mathématique est un ...... ble elliptique est intégrable.
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البلياردو الديناميكي نظام دينا ...... ه ينعكس منه بدون فقدان السرعة.
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title
Billiards
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Billiards
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A dynamical billiard is a dyna ...... nown as outer billiard theory.
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Dynamisches Billard wird ein d ...... aher ein Hamiltonsches System.
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Um bilhar dinâmico é um sistem ...... ricção sobre uma superfície é:
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Un billar dinámico es un siste ...... r contenidos dentro de una reg
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Un billard mathématique est un ...... s'appelle la théorie du billar
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البلياردو الديناميكي نظام دينا ...... ه ينعكس منه بدون فقدان السرعة.
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Bilhar dinâmico
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Billar dinámico
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Billard (mathématiques)
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Dynamical billiards
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Dynamisches Billard
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البلياردو الديناميكي
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