Abstract
Let M be an n-dimensional Riemann manifold, and \(\Omega \subset \) M a domain with the boundary composed of several smooth hypersurfaces. The billiard [KT1991] inside Ω is a dynamical system where a material point of the unit mass is freely moving inside the domain and obeying the reflection law at the boundary, i.e., having congruent impact and reflection angles with the space tangent to the boundary at any bouncing point. It is also assumed that the reflection is absolutely elastic, i.e., that the velocity of the material point does not change before and after impacts.
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© 2011 Springer Basel AG
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Dragović, V., Radnović, M. (2011). Ellipsoidal Billiards and Their Periodical Trajectories. In: Poncelet Porisms and Beyond. Frontiers in Mathematics. Springer, Basel. https://doi.org/10.1007/978-3-0348-0015-0_7
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DOI: https://doi.org/10.1007/978-3-0348-0015-0_7
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Online ISBN: 978-3-0348-0015-0
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