Limit distribution of the nodal domain number for the right-isosceles triangle billiard

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 (the same as for integrable billiards) and also at . The only...

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Veröffentlicht in:	Theoretical and mathematical physics 2021-04, Vol.207 (1), p.483-486
Hauptverfasser:	Jain, M., Bamal, B., Jain, S. R.
Format:	Artikel
Sprache:	eng
Schlagworte:	14/34 639/766/189 639/766/530 639/766/747 Applications of Mathematics Billiards Distribution functions Domains Mathematical and Computational Physics Physics Physics and Astronomy Probability distribution functions Theoretical
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Zusammenfassung:	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 (the same as for integrable billiards) and also at . The only exact results previously known in this direction correspond to integrable billiards that are separable.
ISSN:	0040-5779 1573-9333
DOI:	10.1134/S0040577921040061