J. Aguilar and J. M. Combes, A class of analytic perturbations for one-body Schr??dinger Hamiltonians, Communications in Mathematical Physics, vol.10, issue.5, pp.269-279, 1971.
DOI : 10.1007/BF01877510

V. I. Arnold and A. Avez, Méthodes ergodiques de la mécanique classique, 1967.

V. Baladi, Anisotropic Sobolev spaces and dynamical transfer operators Algebraic and topological dynamics, Proceedings of the conference Contemporary Mathematics, pp.123-135, 2004.
DOI : 10.1090/conm/385/07194

V. Baladi and M. Tsujii, Espaces anisotropes de types H??lder et Sobolev, Annales de l???institut Fourier, vol.57, issue.1, pp.127-154, 2007.
DOI : 10.5802/aif.2253

E. Balslev and J. M. Combes, Spectral properties of many-body Schr??dinger operators with dilatation-analytic interactions, Communications in Mathematical Physics, vol.12, issue.5, pp.280-294, 1971.
DOI : 10.1007/BF01877511

M. Blank, G. Keller, and C. Liverani, Ruelle??Perron??Frobenius spectrum for Anosov maps, Nonlinearity, vol.15, issue.6, pp.1905-1973, 2002.
DOI : 10.1088/0951-7715/15/6/309

URL : http://arxiv.org/abs/nlin/0104031

C. Bonatti and N. Guelman, Transitive Anosov flows and Axiom-A diffeomorphisms, Ergodic Theory and Dynamical Systems, vol.19, issue.03, pp.817-848, 2009.
DOI : 10.2307/2373372

D. Borthwick, Spectral theory of infinite-area hyperbolic surfaces, 2007.
DOI : 10.1007/978-3-319-33877-4

M. Brin and G. Stuck, Introduction to Dynamical Systems, 2002.
DOI : 10.1017/CBO9780511755316

O. Butterley and C. Liverani, Smooth Anosov flows: correlation spectra and stability, Journal of Modern Dynamics, vol.1, issue.2, pp.301-322, 2007.
DOI : 10.3934/jmd.2007.1.301

H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon, Schrödinger operators, with application to quantum mechanics and global geometry Texts and Monographs in Physics, 1987.

E. B. Davies, Linear operators and their spectra, 2007.
DOI : 10.1017/CBO9780511618864

D. Dolgopyat, On Decay of Correlations in Anosov Flows, The Annals of Mathematics, vol.147, issue.2, pp.357-390, 1998.
DOI : 10.2307/121012

D. Dolgopyat, On mixing properties of compact group extensions of hyperbolic systems, Israel Journal of Mathematics, vol.110, issue.188, pp.157-205, 2002.
DOI : 10.1007/BF02764076

F. Faure, Semiclassical spectral gap for transfer operators of partially expanding map. preprint:hal-00368190, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00368190

F. Faure and N. Roy, Ruelle???Pollicott resonances for real analytic hyperbolic maps, Nonlinearity, vol.19, issue.6, pp.1233-1252, 2006.
DOI : 10.1088/0951-7715/19/6/002

F. Faure, N. Roy, and J. Sjöstrand, Semi-classical approach for Anosov diffeomorphisms and Ruelle resonances, The Open Mathematics Journal, vol.1, issue.1, pp.35-81, 2008.
DOI : 10.2174/1874117400801010035

URL : https://hal.archives-ouvertes.fr/hal-00383044

M. Field, I. Melbourne, and A. Török, Stability of mixing and rapid mixing for hyperbolic flows, Annals of Mathematics, vol.166, issue.1, pp.269-291, 2007.
DOI : 10.4007/annals.2007.166.269

C. Gérard and J. Sjöstrand, Resonances en limite semiclassique et exposants de Lyapunov, Communications in Mathematical Physics, vol.12, issue.2, pp.193-213, 1988.
DOI : 10.1007/BF01225255

E. Ghys, Flots d'Anosov dont les feuilletages stables sont diff??rentiables, Annales scientifiques de l'??cole normale sup??rieure, vol.20, issue.2, pp.251-270, 1987.
DOI : 10.24033/asens.1532

URL : http://archive.numdam.org/article/ASENS_1987_4_20_2_251_0.pdf

E. Ghys, D??formations de flots d'Anosov et de groupes fuchsiens, Annales de l???institut Fourier, vol.42, issue.1-2, pp.209-247, 1992.
DOI : 10.5802/aif.1290

S. Gouzel and C. Liverani, Banach spaces adapted to Anosov systems. Ergodic Theory and dynamical systems, pp.189-217, 2005.

A. Grigis and J. Sjöstrand, Microlocal analysis for differential operators Lecture Note Series, 1994.
DOI : 10.1017/cbo9780511721441

L. Guillope, K. Lin, and M. Zworski, The Selberg Zeta Function for Convex Co-Compact Schottky Groups, Communications in Mathematical Physics, vol.46, issue.1, pp.149-176, 2004.
DOI : 10.1007/s00220-003-1007-1

URL : https://hal.archives-ouvertes.fr/hal-00000036

B. Helffer and J. Sjöstrand, Résonances en limite semi-classique. (resonances in semiclassical limit) Memoires de, p.25, 1986.
DOI : 10.24033/msmf.327

URL : http://archive.numdam.org/article/MSMF_1986_2_24-25__1_0.pdf

M. Hitrik and J. Sjöstrand, Rational invariant tori, phase space tunneling, and spectra for non-selfadjoint operators in dimension 2. Ann. Scient. de l'´ ecole normale supérieure. arXiv:math, pp.703394-703395, 2008.

S. Hurder and A. Katok, Differentiability, rigidity and Godbillon-Vey classes for Anosov flows, Publications math??matiques de l'IH??S, vol.130, issue.1, pp.5-61, 1990.
DOI : 10.1007/BF02699130

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.127.2685

A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, 1995.
DOI : 10.1017/CBO9780511809187

P. Leboeuf, Periodic orbit spectrum in terms of Ruelle-Pollicott resonances, Physical Review E, vol.69, issue.2, p.26204, 2004.
DOI : 10.1103/PhysRevE.69.026204

URL : https://hal.archives-ouvertes.fr/hal-00002290

C. Liverani, On contact Anosov flows, Annals of Mathematics, vol.159, issue.3, pp.1275-1312, 2004.
DOI : 10.4007/annals.2004.159.1275

C. Liverani, Fredholm determinants, anosov maps and ruelle resonances. Discrete and Continuous Dynamical Systems, pp.1203-1215, 2005.
DOI : 10.3934/dcds.2005.13.1203

URL : http://arxiv.org/abs/math/0505049

A. Martinez, An Introduction to Semiclassical and Microlocal Analysis, 2002.
DOI : 10.1007/978-1-4757-4495-8

D. Mcduff and D. Salamon, Introduction to symplectic topology, 1998.

S. Nonnenmacher, Some open questions in ???wave chaos???, Nonlinearity, vol.21, issue.8, pp.113-121, 2008.
DOI : 10.1088/0951-7715/21/8/T01

URL : https://hal.archives-ouvertes.fr/hal-00282243

S. Nonnenmacher and M. Zworski, Distribution of Resonances for Open Quantum Maps, Communications in Mathematical Physics, vol.33, issue.2, pp.311-365, 2007.
DOI : 10.1007/s00220-006-0131-0

URL : https://hal.archives-ouvertes.fr/hal-00004901

Y. Pesin, Lectures on Partial Hyperbolicity and Stable Ergodicity, 2004.
DOI : 10.4171/003

M. Reed and B. Simon, Mathematical methods in physics, vol I : Functional Analysis. Academic press, 1972.

M. Reed and B. Simon, Mathematical methods in physics, vol IV : Analysis of operators, 1978.

D. Ruelle, Thermodynamic formalism. The mathematical structures of classical equilibrium . Statistical mechanics, 1978.

D. Ruelle, Locating resonances for AxiomA dynamical systems, Journal of Statistical Physics, vol.32, issue.No. 4, pp.281-292, 1986.
DOI : 10.1007/BF01011300

A. Salva, Lectures on Symplectic Geometry, 2001.

J. Sjöstrand, Geometric bounds on the density of resonances for semiclassical problems . Duke Math, J, vol.60, issue.1, pp.1-57, 1990.

J. Sjöstrand, Density of resonances for strictly convex analytic obstacles, With an appendix by M. Zworski. [44] J. Sjöstrand. Lecture on resonances. Available on http, pp.397-447, 1996.
DOI : 10.4153/CJM-1996-022-9

J. Sjöstrand, Resonances associated to a closed hyperbolic trajectory in dimension 2, Asymptotic Anal, vol.36, issue.2, pp.93-113, 2003.

J. Sjöstrand and M. Zworski, Fractal upper bounds on the density of semiclassical resonances, Duke Mathematical Journal, vol.137, issue.3, pp.381-459, 2007.
DOI : 10.1215/S0012-7094-07-13731-1

M. Tsujii, Decay of correlations in suspension semi-flows of angle-multiplying maps. Ergodic Theory and Dynamical Systems, pp.291-317, 2008.

M. Tsujii, Quasi-compactness of transfer operators for contact Anosov flows, Nonlinearity, vol.23, issue.7, 2008.
DOI : 10.1088/0951-7715/23/7/001

M. W. Wong, An introduction to pseudo-differential operators, 1999.
DOI : 10.1142/4047

J. Wunsch and M. Zworski, The FBI transform on compact C ? manifolds, Transactions of the American Mathematical Society, vol.353, issue.03, pp.1151-1167, 2001.
DOI : 10.1090/S0002-9947-00-02751-3

S. Zelditch, Quantum Ergodicity and Mixing of Eigenfunctions, 2005.
DOI : 10.1016/B0-12-512666-2/00332-1

M. Zworski, Resonances in physics and geometry. Notices of the A, 1999.