Geodesic
Limit distribution of the~nodal domain number for the~right-isosceles triangle billiard
Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 1, pp. 99-103

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We present the probability distribution function of the nodal domain number for the right-isosceles triangle billiard. This is the first explicit result for a nonseparable plane polygonal billiard. The distribution function has a peak at $2/\pi$ (the same as for integrable billiards) and also at $2\sqrt{2}/\pi$. The only exact results previously known in this direction correspond to integrable billiards that are separable.
Mots-clés : billiard, limit distribution
Keywords: integrable system. 
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     author = {M. Jain and B. Bamal and S. R. Jain},
     title = {Limit distribution of the~nodal domain number for the~right-isosceles triangle billiard},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
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     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_207_1_a5/}
}
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M. Jain; B. Bamal; S. R. Jain. Limit distribution of the~nodal domain number for the~right-isosceles triangle billiard. Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 1, pp. 99-103. http://geodesic.mathdoc.fr/item/TMF_2021_207_1_a5/