Retroreflecting Curves in Nonstandard Analysis - Almeida, R.; Neves, V.; Plakhov, A. (Журнал математичної фізики, аналізу, геометрії, 2009)
We present a direct construction of retroreflecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class $C^1$, 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.