E. Akkermans, G. V. Dunne, and A. Teplyaev, Physical consequences of complex dimensions of fractals, EPL (Europhysics Letters), vol.88, issue.4, p.40007, 2009.
DOI : 10.1209/0295-5075/88/40007

S. Arrhenius, On the reaction velocity of the inversion of cane sugar by acids 4:226, 1889, German. Translated and published in: Selected Readings in, 1967.

Y. Bakhtin, Exit asymptotics for small diffusion about an unstable equilibrium. Stochastic Process, Appl, vol.118, issue.5, pp.839-851, 2008.

Y. Bakhtin, Noisy heteroclinic networks. Probab. Theory Related Fields, pp.1-42, 2011.
DOI : 10.1007/s00440-010-0264-0

URL : http://arxiv.org/abs/0712.3952

Y. Bakhtin, Gumbel distribution in exit problems, 2013.

Y. Bakhtin, On Gumbel limit for the length of reactive paths, Stochastics and Dynamics, vol.15, issue.01, 2014.
DOI : 10.1142/S021949371550001X

A. A. Balkema and L. De-haan, Residual Life Time at Great Age, The Annals of Probability, vol.2, issue.5, pp.792-804, 1974.
DOI : 10.1214/aop/1176996548

G. B. Arous, S. Kusuoka, and D. W. Stroock, The Poisson kernel for certain degenerate elliptic operators, Journal of Functional Analysis, vol.56, issue.2, pp.171-209, 1984.
DOI : 10.1016/0022-1236(84)90086-7

N. Berglund, Kramers' law: Validity, derivations and generalisations, Markov Process. Related Fields, vol.19, issue.3, pp.459-490, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00604399

N. Berglund and B. Gentz, On the Noise-Induced Passage Through an Unstable Periodic Orbit I: Two-Level Model, Journal of Statistical Physics, vol.114, issue.5/6, pp.1577-1618, 2004.
DOI : 10.1023/B:JOSS.0000013966.54504.da

URL : https://hal.archives-ouvertes.fr/hal-00003007

N. Berglund and B. Gentz, Universality of first-passage- and residence-time distributions in non-adiabatic stochastic resonance, Europhysics Letters (EPL), vol.70, issue.1, pp.1-7, 2005.
DOI : 10.1209/epl/i2004-10472-2

N. Berglund and B. Gentz, Noise-induced phenomena in slow?fast dynamical systems. A sample-paths approach. Probability and its Applications, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00010168

N. Berglund and B. Gentz, On the Noise-Induced Passage through an Unstable Periodic Orbit II: General Case, SIAM Journal on Mathematical Analysis, vol.46, issue.1, pp.310-352, 2014.
DOI : 10.1137/120887965

URL : https://hal.archives-ouvertes.fr/hal-00723729

G. Birkhoff, Extensions of Jentzsch's theorem, Trans. Amer. Math. Soc, vol.85, pp.219-227, 1957.

N. N. Bogoliubov, On a new form of adiabatic perturbation theory in the problem of particle interaction with a quantum field, 1956.

F. Cérou, A. Guyader, T. Lelì, and F. Malrieu, On the length of one-dimensional reactive paths, ALEA, Lat. Am. J. Probab. Math. Stat, vol.10, issue.1, pp.359-389, 2013.

O. Costin and G. Giacomin, Oscillatory Critical Amplitudes in Hierarchical Models and the Harris Function of Branching Processes, Journal of Statistical Physics, vol.73, issue.3, pp.471-486, 2013.
DOI : 10.1007/s10955-012-0609-4

URL : https://hal.archives-ouvertes.fr/hal-00936843

M. V. Day, On the exponential exit law in the small parameter exit problem, Stochastics, vol.17, issue.4, pp.297-323, 1983.
DOI : 10.1080/17442508308833244

M. V. Day, Some phenomena of the characteristic boundary exit problem In Diffusion processes and related problems in analysis, Progr. Probab. Birkhäuser Boston, vol.22, pp.55-71, 1989.

M. V. Day, Conditional Exits for Small Noise Diffusions with Characteristic Boundary, The Annals of Probability, vol.20, issue.3, pp.1385-1419, 1992.
DOI : 10.1214/aop/1176989696

M. V. Day, Cycling and skewing of exit measures for planar systems, Stochastics and Stochastic Reports, vol.50, issue.3-4, pp.227-247, 1994.
DOI : 10.1080/17442509408833907

M. V. Day, On the exit law from saddle points. Stochastic Process, Appl, vol.60, pp.287-311, 1995.

M. V. Day, Exit cycling for the Van der Pol oscillator and quasipotential calculations, Journal of Dynamics and Differential Equations, vol.16, issue.4, pp.573-601, 1996.
DOI : 10.1007/BF02218845

F. A. De-moura, U. Tirnakli, and M. L. Lyra, Convergence to the critical attractor of dissipative maps: Log-periodic oscillations, fractality, and nonextensivity, Physical Review E, vol.62, issue.5, pp.6361-6365, 2000.
DOI : 10.1103/PhysRevE.62.6361

B. Derrida and G. Giacomin, Log-periodic Critical Amplitudes: A Perturbative Approach, Journal of Statistical Physics, vol.73, issue.1-2, pp.286-304, 2014.
DOI : 10.1007/s10955-013-0774-0

B. Derrida, C. Itzykson, and J. M. Luck, Oscillatory critical amplitudes in hierarchical models, Communications in Mathematical Physics, vol.16, issue.1, pp.115-132, 1984.
DOI : 10.1007/BF01212352

B. Doucot, W. Wang, J. Chaussy, B. Pannetier, R. Rammal et al., First Observation of the Universal Periodic Corrections to Scaling: Magnetoresistance of Normal-Metal Self-Similar Networks, Physical Review Letters, vol.57, issue.10, pp.1235-1238, 1986.
DOI : 10.1103/PhysRevLett.57.1235

G. V. Dunne, Heat kernels and zeta functions on fractals, Journal of Physics A: Mathematical and Theoretical, vol.45, issue.37, p.45374016, 2012.
DOI : 10.1088/1751-8113/45/37/374016

W. E. and E. Vanden-eijnden, Towards a theory of transition paths, J. Stat. Phys, vol.123, issue.3, pp.503-523, 2006.

H. Eyring, The Activated Complex in Chemical Reactions, The Journal of Chemical Physics, vol.3, issue.2, pp.107-115, 1935.
DOI : 10.1063/1.1749604

R. A. Fisher and L. H. Tippett, Limiting forms of the frequency distribution of the largest or smallest member of a sample, Proc. Camb, p.180190, 1928.
DOI : 10.1017/S0305004100015681

M. Fréchet, Sur la loi de probabilité de l'´ ecart maximum, Annales de la société polonaise de Mathématiques, p.93, 1927.

I. Fredholm, Sur une classe d?????quations fonctionnelles, Acta Mathematica, vol.27, issue.0, pp.365-390, 1903.
DOI : 10.1007/BF02421317

M. I. Freidlin and A. D. , Random Perturbations of Dynamical Systems, 1998.

S. Getfert and P. Reimann, Suppression of thermally activated escape by heating, Physical Review E, vol.80, issue.3, p.30101, 2009.
DOI : 10.1103/PhysRevE.80.030101

S. Getfert and P. Reimann, Thermally activated escape far from equilibrium: A unified path-integral approach, Chemical Physics, vol.375, issue.23, pp.386-398, 2010.
DOI : 10.1063/1.3569539

D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, 2001.

B. Gnedenko, Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire, The Annals of Mathematics, vol.44, issue.3, pp.423-453, 1943.
DOI : 10.2307/1968974

J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 1990.

M. Hirsch, C. Pugh, and M. Shub, Invariant Manifolds, 1977.

P. Hitczenko and G. Medvedev, Bursting Oscillations Induced by Small Noise, SIAM Journal on Applied Mathematics, vol.69, issue.5, pp.1359-1392, 2009.
DOI : 10.1137/070711803

URL : http://arxiv.org/abs/0712.4074

P. Hitczenko and G. Medvedev, The Poincar?? Map of Randomly Perturbed Periodic Motion, Journal of Nonlinear Science, vol.3, issue.3, pp.835-861, 2013.
DOI : 10.1007/s00332-013-9170-9

]. R. Jentzsch, ¨ Uber Integralgleichungen mit positivem Kern, J. f. d. reine und angew. Math, vol.141, pp.235-244, 1912.

Y. Kifer, The exit problem for small random perturbations of dynamical systems with a hyperbolic fixed point, Israel Journal of Mathematics, vol.17, issue.1, pp.74-96, 1981.
DOI : 10.1007/BF02761819

H. A. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions, Physica, vol.7, issue.4, pp.284-304, 1940.
DOI : 10.1016/S0031-8914(40)90098-2

M. G. Kre?-in and M. A. Rutman, Linear operators leaving invariant a cone in a Banach space, Uspehi Matem. Nauk, pp.3-95, 1948.

J. Lu and J. Nolen, Reactive trajectories and the transition path process. Probability Theory and Related Fields, pp.1-50, 2014.

R. S. Maier and D. L. Stein, Oscillatory Behavior of the Rate of Escape through an Unstable Limit Cycle, Physical Review Letters, vol.77, issue.24, pp.4860-4863, 1996.
DOI : 10.1103/PhysRevLett.77.4860

A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization, a universal concept in nonlinear sciences, volume 12 of Cambridge Nonlinear Science Series, 2001.

L. C. Rogers and D. Williams, Diffusions, Markov processes, and martingales Cambridge Mathematical Library, 1994.
DOI : 10.1017/cbo9780511805141

E. Seneta, D. Vere, and -. , On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states, Journal of Applied Probability, vol.1, issue.02, pp.403-434, 1966.
DOI : 10.1093/qmath/13.1.7

D. Sornette, Discrete-scale invariance and complex dimensions, Physics Reports, vol.297, issue.5, pp.239-270, 1998.
DOI : 10.1016/S0370-1573(97)00076-8

URL : http://arxiv.org/abs/cond-mat/9707012

B. Van, A theory of the amplitude of free and forced triode vibration, Radio. Rev, vol.1, p.701, 1920.

B. Van, On relaxation oscillation, Phil. Mag, vol.2, pp.978-992, 1926.
URL : https://hal.archives-ouvertes.fr/jpa-00253137

B. Van, Forced oscillations in a circuit with non-linear resistance. (Reception with reactive triode), Phil. Mag, vol.3, pp.64-80, 1927.

E. Vanden-eijnden, Transition Path Theory, volume 703 of Lecture Notes in Physics, 2006.

F. Verhulst, Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics, 2005.
DOI : 10.1007/0-387-28313-7

A. M. Yaglom, Certain limit theorems of the theory of branching random processes. Doklady Akad, Nauk SSSR (N.S.), vol.56, pp.795-798, 1947.

B. P. Bâtiment-de-mathématiques, 6759 45067 Orléans Cedex 2, France E-mail address: nils.berglund@univ-orleans