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- W2950027763 abstract "The famous conjecture of V.Ya.Ivrii (1978) says that {it in every billiard with infinitely-smooth boundary in a Euclidean space the set of periodic orbits has measure zero}. In the present paper we study the complex version of Ivrii's conjecture for odd-periodic orbits in planar billiards, with reflections from complex analytic curves. We prove positive answer in the following cases: 1) triangular orbits; 2) odd-periodic orbits in the case, when the mirrors are algebraic curves avoiding two special points at infinity, the so-called isotropic points. We provide immediate applications to the real piecewise-algebraic Ivrii's conjecture and to its analogue in the invisibility theory." @default.
- W2950027763 created "2019-06-27" @default.
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- W2950027763 date "2013-09-07" @default.
- W2950027763 modified "2023-09-25" @default.
- W2950027763 title "On odd-periodic orbits in complex planar billiards" @default.
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