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Séminaire Équations aux dérivées partielles (Polytechnique)

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V. Petkov
Sur la conjecture de Lax et Phillips pour un nombre fini d'obstacles strictement convexes
Séminaire Équations aux dérivées partielles (Polytechnique) (1995-1996), Exp. No. 11, 13 p.
Article PDF | Analyses Zbl 0884.35084 | 1 citation dans Cedram

Bibliographie

[BGR] C. Bardos, J.C. Guillot, J. Ralston, La relation de Poisson pour l'équation des ondes dans un ouvert non-borné, Commun. Partial Diff. Equations 7 (1982), 905-958.  MR 668585 |  Zbl 0496.35067
[BL] M. Babillot and F. Ledrappier, Lalley's theorem on periodic orbits of hyperbolic flows, Preprint, Ecole Polytechnique, 1996.  Zbl 0915.58074
[Be] V. Bernstein, Leçons sur les progrés récents de la théorie des séries de Dirichlet, Paris, Gauthier-Villards, 1933.  Zbl 0008.11503
[Bu] N. Burq, Controle de l'équation des plaques en présence d'obstacles strictement convexes, Suppl. Bull. Soc. Math. France, Mémoire n° 55, 121 (1993), . Numdam |  Zbl 0930.93007
[F1] L. Farhy, Distribution near real axis of the scattering poles generated by a non-hyperbolic ray, Ann. Inst. H. Poincaré (Physique théorique), 60 (1994), 291-302. Numdam |  MR 1281648 |  Zbl 0808.35091
[F2] L. Farhy, Lower bounds on the number of scattering poles under lines parallel to the real axis, Commun. Partial Diff. Equations, 20 (1995), 729-740.  MR 1326904 |  Zbl 0822.35105
[G] C. Gérard, Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes, Bull. de S.M.F., Mémoire n° 31, 116 (1988). Numdam |  MR 998698 |  Zbl 0654.35081
[GM] V. Guillemin and R. Melrose, The Poisson summation formula for manifolds with boundary, Adv. in Math. 32 (1979), 128-148.  MR 539531 |  Zbl 0415.35062
[H] N.T. Haydn, Meromorphic extensions of the zeta function for Axiom A flows, Ergod. Th. & Dynam. Sys., 10 (1990), 347-360.  MR 1062762 |  Zbl 0694.58035
[I1] M. Ikawa, Decay of solutions of the wave equation in the exterior of two convex obstacles, Osaka J. Math. 19 (1982), 459-509.  MR 676233 |  Zbl 0498.35008
[I2] M. Ikawa, Trapping obstacles with a sequence of poles of the scattering matrix converging to the real axis, Osaka J. Math. 22 (1985), 657-689.  MR 815439 |  Zbl 0617.35102
[I3] M. Ikawa, Decay of solutions of the wave equation in the exterior of several strictly convex bodies, Ann. Inst. Fourier 38 (1988), 113-146. Cedram |  MR 949013 |  Zbl 0636.35045
[I4] M. Ikawa, On the existence of the poles of the scattering matrix for several convex obstacles, Proc. Japan Acad., Ser. A, 64 (1988), 69-102.  Zbl 0637.35068
[I5] M. Ikawa, On the distribution of poles of the scattering matrix for several convex bodies, pp. 210-225 in Lecture Notes in Mathematics, vol. 1450, Springer, Berlin, 1990.  MR 1084611 |  Zbl 0754.35103
[I6] M. Ikawa, Singular perturbation of symbolic flows and poles of the zeta function, Osaka J. Math. 27 (1990), 281-300 and 29 (1992), 161-174.  MR 1066627 |  Zbl 0708.58019
[I7] M. Ikawa, On Zeta function and scattering poles for several convex bodies, Exposé II, Journées Equtions aux Dérivées Partielles, Saint-Jean-de-Monts, Juin 1994. Cedram |  MR 1298673 |  Zbl 0872.58048
[LP] P. Lax and R. Phillips, Scattering Theory, New York, Academic Press 1967.  MR 217440 |  Zbl 0186.16301
[M1] R. Melrose, Polynomial bound on number of scattering poles, J. Funct. Anal., 53 (1983), 29-40.  MR 724031 |  Zbl 0535.35067
[M2] R. Melrose, Polynomial bound on the distribution of poles in scattering by an obstacle, Journées Equations aux Dérivées Partielles, Saint-Jean-de-Monts, 1984. Cedram |  Zbl 0621.35073
[MS] R. Melrose and J. Sjöstrand, Singularities in boundary value problems, I, II. Comm. Pure Appl. Math. 31 (1978), 593-617 and 35 (1982), 129-168.  Zbl 0546.35083
[PP] W. Parry and M. Pollicott, Zeta functions and periodic orbits structure of hyperbolic dynamics, Astérique, 187-188, Soc. Math. de France, 1990.  MR 1085356 |  Zbl 0726.58003
[PS1] V. Petkov and L. Stoyanov, Periods of multiple reflecting geodesics and inverse spectal results, Amer. J. Math. 109 (1987), 617-668.  MR 900034 |  Zbl 0652.35027
[PS2] V. Petkov and L. Stoyanov, Geometry of Reflecting Rays and Inverse Spectral Problems, Chichester, John Wiley & Sons 1992.  MR 1172998 |  Zbl 0761.35077
[PV] V. Petkovand G. Vodev, Upper bound on the number of the scattering poles and the Lax-Phillips conjecture, Asymptotic Analysis 7 (1993), 97-104.  MR 1225440 |  Zbl 0801.35099
[Po] M. Pollicott, Meromorphic extensions of generalized zeta functions, Invent. Math. 85 (1986), 147-164.  MR 842051 |  Zbl 0604.58042
[SjZ1] J. Sjötrand and M. Zworski, Complex scaling and the distribution of scattering poles, J. Amer. Math. Soc. 4 (1991), 729-769.  MR 1115789 |  Zbl 0752.35046
[SjZ2] J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles, Commun. Partial Diff. Equations 18 (1993), 847-857.  MR 1218521 |  Zbl 0784.35070
[Ste] Pl. Stefanov, Stability of the resonances under smooth perturbations of the boundary, Asymptotic Analysis, 9 (1994), 291-296.  MR 1295296 |  Zbl 0814.35022
[St1] L. Stoyanov, Poisson relation for the scattering kernel and inverse scattering by obstacles, Séminaire EDP, Exposé V, Ecole Polytechnique, 1994-1995. Cedram |  MR 1362553 |  Zbl 0888.58070
[St2] L. Stoyanov, Exponential instability for a class of dispersing billiards, Preprint, Mathematics Department, University of Western Australia, 1995.  MR 1677157 |  Zbl 0923.58028
[St3] L. Stoyanov, Generalized Hamiltonian flow and rigidity of the scattering length spectrum, Preprint, Mathematics Department, University of Western Australia, 1996.
[Va] B. Vainberg, Asymptotic Methods of Mathematical Physics, Gordon and Breach Sci. Publ. New York, 1988.  Zbl 0743.35001
[Vo1] G. Vodev, Sharp bounds on the number of scattering poles for perturbations of the Laplacian, Comm. Math. Phys. 146 (1992), 205-216. Article |  MR 1163673 |  Zbl 0766.35032
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