Abstract
We consider focusing curves Γf (of class C∝, α≥3) such that each incoming infinitesimal beam of parallel rays focuses after hitting Γf for the last time in the series of consecutive reflections from it. We call such curves absolutely focusing. We prove some characteristic properties of absolutely focusing curves and show that these remain absolutely focusing under small C3-(C4)-perturbations if this component has constant (nonconstant) curvature. We also present examples of absolutely focusing curves and consider the applications of these curves to some classes of continuous fractions.
On leave from: Institute of Oceanology of Ac. Sci. USSR, ul. Krasikova 23, 117218 Moscow, USSR
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© 1992 Springer-Verlag
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Bunimovich, L.A. (1992). On absolutely focusing mirrors. In: Krengel, U., Richter, K., Warstat, V. (eds) Ergodic Theory and Related Topics III. Lecture Notes in Mathematics, vol 1514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097528
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DOI: https://doi.org/10.1007/BFb0097528
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