Farhy, Leon S. Distribution near the real axis of scattering poles generated by a non- hyperbolic periodic ray. (English) Zbl 0808.35091 Ann. Inst. Henri Poincaré, Phys. Théor. 60, No. 3, 291-302 (1994). Summary: We prove lower bounds in small neighborhoods of the real axis on the number of scattering poles for a trapping obstacle with unique periodic non-hyperbolic ray. The periodic ray is such that all eigenvalues of the corresponding Poincaré map are equal to one. Cited in 3 Documents MSC: 35P25 Scattering theory for PDEs 35L05 Wave equation Keywords:lower bounds; number of scattering poles × Cite Format Result Cite Review PDF Full Text: Numdam EuDML References: [1] C. Bardos , J.C. Guillot , J. Ralston , La relation de Poisson pour l’équation des ondes dans un ouvert non borné , Comm. Part. Diff. Eq. , Vol. 7 , 1982 , pp. 905 - 958 . MR 668585 | Zbl 0496.35067 · Zbl 0496.35067 · doi:10.1080/03605308208820241 [2] C. Gérard , Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes , Bull. S.M.F. , T 116 , Mémoire n^\circ 31 , 1988 . Numdam | MR 998698 | Zbl 0654.35081 · Zbl 0654.35081 [3] M. Ikawa , On the poles of the scattering matrix for two strictly convex obstacles , J. Math. Kyoto Univ. , Vol. 23 , 1983 , pp. 127 - 194 . Article | MR 692733 | Zbl 0561.35060 · Zbl 0561.35060 [4] M. Ikawa , Trapping obstacles with a sequence of poles of the scattering matrix converging to the real axis , Osaka J. Math. , Vol. 22 , 1985 , pp. 657 - 689 . MR 815439 | Zbl 0617.35102 · Zbl 0617.35102 [5] M. Ikawa , preprint. [6] P.D. Lax , R.S. Phillips , Scattering theory , Academic Press , New York , 1967 . MR 217440 | Zbl 0186.16301 · Zbl 0186.16301 [7] R.B. Melrose , Scattering theory and the trace of the wave group , J. of Funct. Anal. , Vol. 45 , 1982 , pp. 29 - 40 . MR 645644 | Zbl 0525.47007 · Zbl 0525.47007 · doi:10.1016/0022-1236(82)90003-9 [8] J. Sjöstrand , M. Zworski , Lower bounds on the number of scattering poles , Comm. P.D.E. , Vol. 18 , 1993 , pp. 847 - 854 . MR 1218521 | Zbl 0784.35070 · Zbl 0784.35070 · doi:10.1080/03605309308820953 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.