Retroreflecting Curves in Nonstandard Analysis
Ключові слова:Nonstandard Analysis, retroreflectors, maximum resistance problems, reflection, billiards.
АнотаціяWe present a direct construction of retroreflecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class C1, except for a hyper-finite set of values, such that the probability of a particle being reflected from the curve with the velocity opposite to the velocity of incidence, is infinitely close to 1. The constructed curves are of two kinds: a curve infinitely close to a straight line and a curve infinitely close to the boundary of a bounded convex set. We shall see that the latter curve is a solution of the problem: find the curve of maximum resistance infinitely close to a given curve.
Mathematics Subject Classification: 26E35, 49K30, 49Q10.
Almeida, R.; Neves, V.; Plakhov, A. Retroreflecting Curves in Nonstandard Analysis. Журн. мат. фіз. анал. геом. 2009, 5, 12-24.
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