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ÆÓÐÍÀËÛ // Symmetry, Integrability and Geometry: Methods and Applications

SIGMA, 2011, òîì 7, 080, 8 ñòð. (Mi sigma638)

The 2-Transitive Transplantable Isospectral Drums
Jeroen Schillewaert, Koen Thas

Ñïèñîê ëèòåðàòóðû

1. Brooks R., Tse R., “Isospectral surfaces of small genus”, Nagoya Math. J., 107 (1987), 13–24  mathscinet  zmath  isi
2. Buser P., “Isospectral Riemann surfaces”, Ann. Inst. Fourier (Grenoble), 36 (1986), 167–192  crossref  mathscinet  zmath
3. Buser P., Conway J., Doyle P., Semmler K.-D., “Some planar isospectral domains”, Int. Math. Res. Not., 1994:9 (1994), 391–400  crossref  mathscinet  zmath; arXiv: 1005.1839
4. Cameron P.J., “Finite permutation groups and finite simple groups”, Bull. London Math. Soc., 13 (1981), 1–22  crossref  mathscinet  zmath  isi
5. Conway J.H., Curtis R.T., Norton S.P., Parker R.A., Wilson R.A., Atlas of finite groups. Maximal subgroups and ordinary characters for simple groups, with computational assistance from J.G. Thackray, Oxford University Press, Eynsham, 1985  mathscinet  zmath
6. Dixon J.D., Mortimer B., Permutation groups, Graduate Texts in Mathematics, 163, Springer-Verlag, New York, 1996  mathscinet  zmath
7. Epkenhans M., Gerstengarbe O., “On the Galois number and the minimal degree of doubly transitive groups”, Comm. Algebra, 28 (2000), 4889–4900  crossref  mathscinet  zmath  isi
8. Giraud O., “Finite geometries and diffractive orbits in isospectral billiards”, J. Phys. A: Math. Gen., 38 (2005), L477–L483  crossref  mathscinet  adsnasa  isi; arXiv: nlin.CD/0503069
9. Giraud O., Thas K., “Hearing shapes of drums – mathematical and physical aspects of isospectrality”, Rev. Modern Phys., 82 (2010), 2213–2255  crossref  mathscinet  adsnasa  isi; arXiv: 1101.1239
10. Gordon C., Webb D., Wolpert S., “Isospectral plane domains and surfaces via Riemannian orbifolds”, Invent. Math., 110 (1992), 1–22  crossref  mathscinet  zmath  adsnasa  isi
11. Kac M., “Can one hear the shape of the drum?”, Amer. Math. Monthly, 73:4, part II (1966), 1–23  crossref  mathscinet  zmath
12. Milnor J., “Eigenvalues of the Laplace operators on certain manifolds”, Proc. Nat. Acad. Sci. USA, 51 (1964), 542  crossref  mathscinet  zmath  adsnasa
13. Okada Y., Shudo A., “Equivalence between isospectrality and isolength spectrality for a certain class of planar billiard domains”, J. Phys. A: Math. Gen., 34 (2001), 5911–5922  crossref  mathscinet  zmath  adsnasa  isi; arXiv: nlin.CD/0105068
14. Segre B., Lectures on modern geometry, with an appendix by Lucio Lombardo-Radice, Consiglio Nazionale delle Ricerche Monografie Matematiche, 7, Edizioni Cremonese, Rome, 1961  mathscinet  zmath
15. Sunada T., “Riemannian coverings and isospectral manifolds”, Ann. of Math. (2), 121 (1980), 169–186  crossref  mathscinet  isi
16. Thas K., “Kac's question, planar isospectral pairs and involutions in projective space”, J. Phys. A: Math. Gen., 39 (2006), L385–L388  crossref  mathscinet  zmath  adsnasa  isi
17. Thas K., “Kac's question, planar isospectral pairs and involutions in projective space. II. Classification of generalized projective isospectral data”, J. Phys. A: Math. Gen., 39 (2006), 13237–13242  crossref  mathscinet  zmath  adsnasa  isi
18. Thas K., “$\mathrm{PSL}_n(q)$ as operator group of isospectral drums”, J. Phys. A: Math. Gen., 39 (2006), L673–L675  crossref  mathscinet  zmath  adsnasa  isi
19. Thas K., Classification of transplantable isospectral drums in $\mathbb R^2$, in preparation


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