Distribution of resonances for convex co-compact hyperbolic surfaces

 Access to full text

 Full (PDF)

1. [1] Ch. Gérard and J. Sjöstrand, Semiclassical resonances generated by a closed trajectory of hyperbolic type. Comm. Math. Phys. 108 (1987), 391-421. Zbl0637.35027MR88k:58151
2. [2] L. Guillopé, Sur la distribution des longeurs des géodesiques fermées d'une surface compacte à bord totalement géodesique. Duke Math. J. 53 (1986), 827-848. Zbl0611.53042MR88e:11042
3. [3] L. Guillopé, Fonctions Zêta de Selberg et surfaces de géométrie finie. Advanced Studies in Pure Mathematics 21 (1992), 33-70. Zbl0794.58044MR94d:11032
4. [4] L. Guillopé and M. Zworski, Upper bounds on the number of resonances for non-compact Riemann surfaces. J. Func. Anal. 129 (1995), 364-389. Zbl0841.58063MR96b:58116
5. [5] L. Guillopé and M. Zworski, Polynomial bounds on the number of resonances for some complete spaces of constant negative curvature near infinity. Asymp. Anal. 11 (1995), 1-22. Zbl0859.58028MR96h:58172
6. [6] L. Guillopé and M. Zworski, Scattering asymptotics for Riemann surfaces. to appear in Ann. of Math. Zbl0898.58054
7. [7] B. Helffer and J. Sjöstrand, Résonances en limite semi-classique. Mémoires de la S.M.F. 114(3) (1986). Zbl0631.35075
8. [8] M. Ikawa. On the existence of poles of the scattering for several convex bodies. Proc. Japan Acad. 64 (1988), 91-93. Zbl0704.35113MR90i:35211
9. [9] S. Lalley, Renewal theorems in symbolic dynamics with applications to geodesic flows, noneuclidean tesselations and their fractal limits. Acta Math. 163 (1989), 1-55. Zbl0701.58021MR91c:58112
10. [10] R. Mazzeo and R.B. Melrose, Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature. J. Func. Anal. 75 (1987), 260-310. Zbl0636.58034MR89c:58133
11. [11] R. B. Melrose, Geometric Scattering Theory. Cambridge University Press, 1995. Zbl0849.58071MR96k:35129
12. [12] S.J. Patterson, The limit set of a Fuchsian group. Acta Math. 136 (1976), 241-273. Zbl0336.30005MR56 #8841
13. [13] S.J. Patterson, The Laplacian operator on a Riemann surface I, II, III. Compositio Math. 31 (1975), 83-107, 32 (1976), 71-112, and 33 (1976), 227-259. Zbl0342.30011
14. [14] S.J. Patterson and P. Perry, Divisor of the Selberg Zeta function, I. Even dimensions. preprint, 1995. 
15. [15] D. Ruelle, Chaotic evolution and strange attractors. Lezione Lincee, Cambridge University Press, 1989. Zbl0683.58001MR91d:58169
16. [16] J. Sjöstrand, Singularité analytiques microlocales. Astérisque 95 (1982). Zbl0524.35007MR84m:58151
17. [17] J. Sjöstrand, Geometric bounds on the density of resonances for semi-classical problems. Duke Math. J. 60 (1990), 1-57. Zbl0702.35188
18. [18] J. Sjöstrand, Density of resonances for strictly convex analytic obstacles. Can. J. Math. 48(2) (1996), 437-446. Zbl0863.35072MR97j:35117
19. [19] J. Sjöstrand, A trace formula for resonances and application to semi-classical Schrödinger operators, Séminaire EDP, École Polytechnique, Novembre, 1996. 
20. [20] J. Sjöstrand and M. Zworski, Complex scaling and the distribution of scattering poles. J. of Amer. Math. Soc. 4(4) (1991), 729-769. Zbl0752.35046MR92g:35166
21. [21] J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles. Comm. P. D. E. 18 (1993), 847-858. Zbl0784.35070MR94h:35198
22. [22] J. Sjöstrand and M. Zworski, The complex scaling method for scattering by strictly convex obstacles. Ark. Math. 33 (1995), 135-172. Zbl0839.35095MR96f:35127
23. [23] D. Sullivan, The density at infinity of a discrete group of hyperbolic motions. Publ. IHES 50 (1979), 172-202. Zbl0439.30034MR81b:58031
24. [24] M. Zworski, Distribution of scattering poles for scattering on the real line. J. Funct. Anal., 73(2) (1987), 277-296. Zbl0662.34033MR88h:81223
25. [25] M. Zworski, Counting scattering poles. in SPECTRAL AND SCATTERING THEORY. M. Ikawa, ed. Marcel Dekker, 1994. Zbl0823.35139MR95i:35210
26. [26] M. Zworski, Poisson formulæ for resonances, Séminaire EDP, École Polytechnique, Avril, 1997. Zbl1255.35084MR98j:35036
27. [27] M. Zworski, Dimension of the limit set and the density of resonances for convex co-compact hyperbolic surfaces, preprint, 1997. Zbl1016.58014