منابع مشابه
Fagnano Orbits of Polygonal Dual Billiards
Given a convex n-gon P , a Fagnano periodic orbit of the respective dual billiard map is an n-gon Q whose sides are bisected by the vertices of P . For which polygons P does the ratio Area Q/AreaP have the minimal value? The answer is shown to be: for affine-regular polygons. Mathematics Subject Classification (1991): 52-XX.
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We prove a recent theorem by C. Culter: every polygonal outer billiard in the affine plane has a periodic trajectory. This note contains a proof of a recent theorem by Chris Culter; he obtained this result as an undergraduate participant of the 2004 Penn State REU program. A complete account of Culter’s work involving a more general class of maps and a more detailed analysis of their periodic o...
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Using heuristic arguments based on the trace formulas, we analytically calculate the semiclassical two-point correlation form factor for a family of rectangular billiards with a barrier of height irrational with respect to the side of the billiard and located at any rational position p/q from the side. To do this, we first obtain the asymptotic density of lengths for each family of periodic orb...
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Optical mushroom-shaped billiards offer a unique opportunity to isolate and study semiclassical modes concentrated on nondispersive, marginally unstable periodic orbits. Here we show that the openness of the cavity to external electromagnetic fields leads to unanticipated consequences for the far-field radiation pattern, including directional emission. This is mediated by interactions of margin...
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ژورنال
عنوان ژورنال: Pramana
سال: 1997
ISSN: 0304-4289,0973-7111
DOI: 10.1007/bf02845658