Retroreflecting Curves in Nonstandard Analysis

Автор(и)

  • R. Almeida Department of Mathematics, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
  • V. Neves Department of Mathematics, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
  • A. Plakhov Department of Mathematics, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
    Institute of Mathematical and Physical Sciences, University of Aberystwyth, Aberystwyth SY23 3BZ, Ceredigion, UK

Ключові слова:

Nonstandard Analysis, retroreflectors, maximum resistance problems, reflection, billiards

Анотація

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.

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Як цитувати

(1)
Almeida, R.; Neves, V.; Plakhov, A. Retroreflecting Curves in Nonstandard Analysis. Журн. мат. фіз. анал. геом. 2009, 5, 12-24.

Номер

Том 5 № 1 (2009)

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