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On absolutely focusing mirrors

Part of the Lecture Notes in Mathematics book series (LNM,volume 1514)

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.

Keywords

  • Lyapunov Exponent
  • Continuous Fraction
  • Conjugate Point
  • Parallel Beam
  • Integrable Hamiltonian System

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55444-8

  • Online ISBN: 978-3-540-47076-2

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