منابع مشابه
Recurrence and Periodic Billiard Orbits in Polygons
We show that almost all billiard trajectories return parallel to themselves for rank 1, ergodic polygons. Applications are given to the existence of periodic trajectories.
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We show that periodic orbits are dense in the phase space for billiards in polygons for which the angle between each pair of sides is a rational multiple of π.
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A billiard ball, i.e. a point mass, moves inside a polygon Q with unit speed along a straight line until it reaches the boundary ∂Q of the polygon, then instantaneously changes direction according to the mirror law: “the angle of incidence is equal to the angle of reflection,” and continues along the new line (Fig. 1(a)). Despite the simplicity of this description there is much that is unknown ...
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It is shown that the set of 4-period orbits in outer billiard with piecewise smooth convex boundary has an empty interior, provided the boundary is not a parallelogram.
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We consider the outer billiard outside a regular convex polygon. We deal with the case of regular polygons with 3, 4, 5, 6 or 10 sides. We describe the symbolic dynamics of the map and compute the complexity of the language.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2012
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2011.12.012