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Periodic geodesics of generic nonconvex domains in $\mathbf {R}^2$ and the Poisson relation
Author(s):
Vesselin M.
Petkov;
Luchezar
Stojanov
Journal:
Bull. Amer. Math. Soc.
15
(1986),
88-90.
MSC (1985):
Primary 58G25, 35R30
MathSciNet review:
838792
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References:
- 1.
- K. Andersson and R. Melrose, The propagation of singularities along gliding rays, Invent. Math. 41 (1977), 197-232. MR 494322
- 2.
- M. Golubitsky and V. Guillemin, Stable mappings and their singularities, Graduate Texts in Math., vol. 14, Springer-Verlag, Berlin and New York, 1973. MR 341518
- 3.
- V. Guillemin and R. Melrose, The Poisson summation formula for manifolds with boundary, Adv. in Math. 32 (1979), 204-232. MR 539531
- 4.
- V. F. Lazutkin, Convex billiard and eigenfunctions of the Laplace operator, Leningrad University, 1981. (Russian) MR 633153
- 5.
- S. Marvizi and R. Melrose, Spectral invariants of convex planar regions, J. Differential Geom. 17 (1982), 475-502. MR 679068
- 6.
- R. Melrose and J. Sjöstrand, Singularities in boundary value problems. I, II, Comm. Pure Appl. Math. 31 (1978), 593-617; 35 (1982), 129-168.
- 7.
- V. Petkov and P. Vogel, La représentation de l'application de Poincaré correspondant aux rayons périodiques réflechissants, C. R. Acad. Sci. Paris, Sér. A 296 (1983), 633-635. MR 705678
- 8.
- V. Petkov, Propriétés génériques des rayons réflechissants et applicationns aux problèmes spectraux, Séminaire Bony-Sjöstrand-Meyer, École Polytechnique, Centre de Mathématiques, Exposé XII, 1984-1985. MR 819778
- 9.
- V. Petkov and L. Stojanov, Periods of multiple reflecting geodesics and inverse spectral results, preprint. MR 900034
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Additional Information:
DOI:
10.1090/S0273-0979-1986-15445-5
PII:
S 0273-0979(1986)15445-5
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