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- W2964285518 abstract "We prove that for any $epsilon>0$ the growth rate $P_n$of generalized diagonals or periodic orbits of a typical (in theLebesgue measure sense) triangular billiard satisfies:$P_n < Ce^{n^{sqrt{3}-1+epsilon}}$. This provides an explicit subexponential estimate on the triangular billiard complexity andanswers a long-standing open question for typical triangles. Thisalso makes progress towards a solution of Problem 3 in Katok's listof Five most resistant problems in dynamics. The proof usesessentially new geometric ideas and does not rely on the rationalapproximations." @default.
- W2964285518 created "2019-07-30" @default.
- W2964285518 creator A5007087871 @default.
- W2964285518 date "2013-01-01" @default.
- W2964285518 modified "2023-09-26" @default.
- W2964285518 title "Growth of periodic orbits and generalized diagonals for typical triangular billiards" @default.
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- W2964285518 doi "https://doi.org/10.3934/jmd.2013.7.31" @default.
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