M. J. Davis and E. J. Heller, Quantum dynamical tunneling in bound states, The Journal of Chemical Physics, vol.75, issue.1, p.246, 1981.
DOI : 10.1063/1.441832

N. T. Maitra and E. J. Heller, Semiclassical perturbation approach to quantum reflection, Physical Review A, vol.54, issue.6, p.4763, 1996.
DOI : 10.1103/PhysRevA.54.4763

M. V. Berry and K. E. Mount, Semiclassical approximations in wave mechanics, Reports on Progress in Physics, vol.35, issue.1, p.315, 1972.
DOI : 10.1088/0034-4885/35/1/306

N. T. Maitra and E. J. Heller, Barrier Tunneling and Reflection in the Time and Energy Domains: The Battle of the Exponentials, Physical Review Letters, vol.78, issue.16, p.3035, 1997.
DOI : 10.1103/PhysRevLett.78.3035

K. F. Freed, Path Integrals and Semiclassical Tunneling, Wavefunctions, and Energies, The Journal of Chemical Physics, vol.56, issue.2, p.692, 1972.
DOI : 10.1063/1.1677217

T. F. George and W. H. Miller, below the Classical Threshold, The Journal of Chemical Physics, vol.56, issue.11, p.5722, 1972.
DOI : 10.1063/1.1677094

W. H. Miller, Quantum mechanical transition state theory and a new semiclassical model for reaction rate constants, The Journal of Chemical Physics, vol.61, issue.5, p.1823, 1974.
DOI : 10.1063/1.1682181

S. Coleman, Aspects of Symmetry (selected Erice lectures ), 1985.

H. Cruz, A. Hernandez-cabrera, and A. Munoz, Resonant tunnelling of electrons through parabolic quantum wells: an analytical calculation of the transmission coefficient, Semiconductor Science and Technology, vol.6, issue.3, p.218, 1991.
DOI : 10.1088/0268-1242/6/3/013

Y. Zohta, Path-integral approach to resonant tunneling, Physical Review B, vol.41, issue.11, p.7879, 1990.
DOI : 10.1103/PhysRevB.41.7879

W. A. Lin and L. E. Ballentine, Quantum tunneling and regular and irregular quantum dynamics of a driven double-well oscillator, Physical Review A, vol.45, issue.6, p.3637, 1992.
DOI : 10.1103/PhysRevA.45.3637

O. Bohigas, S. Tomsovic, and D. Ullmo, Manifestations of classical phase space structures in quantum mechanics, Physics Reports, vol.223, issue.2, p.43, 1993.
DOI : 10.1016/0370-1573(93)90109-Q

URL : https://hal.archives-ouvertes.fr/in2p3-00014826

J. M. Greene and I. C. , Hamiltonian maps in the complex plane, Physica D: Nonlinear Phenomena, vol.3, issue.3, p.530, 1981.
DOI : 10.1016/0167-2789(81)90038-5

A. Shudo and K. S. Ikeda, Complex Classical Trajectories and Chaotic Tunneling, Physical Review Letters, vol.74, issue.5, p.682, 1995.
DOI : 10.1103/PhysRevLett.74.682

A. Shudo, Y. Ishii, and K. S. Ikeda, Julia sets and chaotic tunneling: I, Journal of Physics A: Mathematical and Theoretical, vol.42, issue.26, p.265101, 2009.
DOI : 10.1088/1751-8113/42/26/265101

S. C. Creagh and N. D. Whelan, Complex Periodic Orbits and Tunneling in Chaotic Potentials, Physical Review Letters, vol.77, issue.25, p.4975, 1996.
DOI : 10.1103/PhysRevLett.77.4975

URL : https://hal.archives-ouvertes.fr/in2p3-00001288

S. Tomsovic and D. Ullmo, Chaos-assisted tunneling, Physical Review E, vol.50, issue.1, p.145, 1994.
DOI : 10.1103/PhysRevE.50.145

URL : https://hal.archives-ouvertes.fr/in2p3-00014991

F. Leyvraz, D. Ullmo, and J. Phys, The level splitting distribution in chaos-assisted tunnelling, Journal of Physics A: Mathematical and General, vol.29, issue.10, p.2529, 1996.
DOI : 10.1088/0305-4470/29/10/030

URL : https://hal.archives-ouvertes.fr/in2p3-00002859

O. Brodier, P. Schlagheck, and D. Ullmo, Resonance-Assisted Tunneling in Near-Integrable Systems, Physical Review Letters, vol.87, issue.6, p.64101, 2001.
DOI : 10.1103/PhysRevLett.87.064101

URL : https://hal.archives-ouvertes.fr/hal-00003456

O. Brodier, P. Schlagheck, and D. Ullmo, Resonance-Assisted Tunneling, Annals of Physics, vol.300, issue.1, p.88, 2002.
DOI : 10.1006/aphy.2002.6281

URL : https://hal.archives-ouvertes.fr/hal-00003447

C. Eltschka and P. Schlagheck, Resonance- and Chaos-Assisted Tunneling in Mixed Regular-Chaotic Systems, Physical Review Letters, vol.94, issue.1, p.14101, 2005.
DOI : 10.1103/PhysRevLett.94.014101

A. Mouchet, C. Eltschka, and P. Schlagheck, Influence of classical resonances on chaotic tunneling, Physical Review E, vol.74, issue.2, p.26211, 2006.
DOI : 10.1103/PhysRevE.74.026211

S. Löck, A. Bäcker, R. Ketzmerick, and P. Schlagheck, Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime, Physical Review Letters, vol.104, issue.11, p.114101, 2010.
DOI : 10.1103/PhysRevLett.104.114101

]. A. Bäcker, R. Ketzmerick, S. Löck, and L. Schilling, Regular-to-Chaotic Tunneling Rates Using a Fictitious Integrable System, Physical Review Letters, vol.100, issue.10, p.104101, 2008.
DOI : 10.1103/PhysRevLett.100.104101

A. Bäcker, R. Ketzmerick, and S. Löck, Direct regular-to-chaotic tunneling rates using the fictitious-integrable-system approach, Physical Review E, vol.82, issue.5, p.56208, 2010.
DOI : 10.1103/PhysRevE.82.056208

V. I. Arnold, Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics, 1989.

A. M. Ozorio-de-almeida, Hamiltonian Systems: Chaos and Quantization, 1988.
DOI : 10.1017/CBO9780511564161

R. T. Swimm and J. B. Delos, Semiclassical calculations of vibrational energy levels for nonseparable systems using the Birkhoff???Gustavson normal form, The Journal of Chemical Physics, vol.71, issue.4, p.1706, 1979.
DOI : 10.1063/1.438521

B. Eckhardt, Birkhoff-Gustavson normal form in classical and quantum mechanics, Journal of Physics A: Mathematical and General, vol.19, issue.15, p.2961, 1986.
DOI : 10.1088/0305-4470/19/15/020

K. Takahashi and N. Saitô, Chaos and Husimi Distribution Function in Quantum Mechanics, Physical Review Letters, vol.55, issue.7, p.645, 1985.
DOI : 10.1103/PhysRevLett.55.645

G. Torres-vega and J. H. Frederick, Quantum mechanics in phase space: New approaches to the correspondence principle, The Journal of Chemical Physics, vol.93, issue.12, p.8862, 1990.
DOI : 10.1063/1.459225

D. W. Mclaughlin, Complex Time, Contour Independent Path Integrals, and Barrier Penetration, Journal of Mathematical Physics, vol.13, issue.8, p.1099, 1972.
DOI : 10.1063/1.1666102

S. Löck, A. Bäcker, and R. Ketzmerick, Coupling of bouncing-ball modes to the chaotic sea and their counting function, Physical Review E, vol.85, issue.1, p.16210, 2012.
DOI : 10.1103/PhysRevE.85.016210

N. Mertig, S. Löck, A. Bäcker, R. Ketzmerick, and A. Shudo, Complex paths for regular-to-chaotic tunnelling rates, EPL (Europhysics Letters), vol.102, issue.1, p.10005, 2013.
DOI : 10.1209/0295-5075/102/10005