M. Peyrard and A. R. Bishop, Statistical mechanics of a nonlinear model for DNA denaturation, Phys. Rev. Lett, vol.62, p.2755, 1989.

M. Peyrard, Nonlinear dynamics and statistical physics of DNA, Nonlinearity, vol.17, pp.1-40, 2004.

T. Dauxois, M. Peyrard, and A. R. Bishop, Entropy-driven DNA denaturation, Phys. Rev. E, vol.47, issue.1, pp.44-47, 1993.

S. Flach and A. Gorbach, Discrete Breathers: Advances in Theory and Applications, Phys. Rep, vol.467, pp.1-116, 2008.

I. Daumont, T. Dauxois, and M. Peyrard, Modulational instability: First step towards energy localization in nonlinear lattices, Nonlinearity, vol.10, pp.617-630, 1997.

M. V. Ivanchenko, O. I. Kanakov, V. D. Shalfeev, and S. Flach, Discrete breathers in transient processes and thermal equilibrium, Phys. D, vol.198, pp.120-135, 2004.

G. Arioli and A. Szulkin, Periodic motions of an infinite lattice of particles: The strongly indefinite case, Ann. Sci. Math. Que´bec, vol.22, pp.97-119, 1998.

S. Aubry, Breathers in nonlinear lattices: Existence, linear stability and quantization, Phys. D, vol.103, pp.201-250, 1997.

S. Aubry, G. Kopidakis, and V. Kadelburg, Variational proof for hard discrete breathers in some classes of Hamiltonian dynamical systems, Discrete Contin. Dyn. Syst. B, vol.1, pp.271-298, 2001.

G. James, Centre manifold reduction for quasilinear discrete systems, J. Nonlinear Sci, vol.13, pp.27-63, 2003.

G. James, B. Sa´nchez-rey, and J. Cuevas, Breathers in inhomogeneous lattices: An analysis via center manifold reduction, Rev. Math. Phys, vol.21, pp.1-59, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00389846

R. S. Mackay and S. Aubry, Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators, Nonlinearity, vol.7, pp.1623-1643, 1994.

A. Pankov, Travelling waves and Periodic Oscillations in Fermi-Pasta-Ulam Lattices, 2005.

J. Sepulchre and R. S. Mackay, Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators, Nonlinearity, vol.10, pp.679-713, 1997.

A. Zevin, Localization of periodic oscillations in discrete non-linear systems, J. Sound Vibration, vol.193, p.847, 1996.

M. Peyrard, S. Cuesta-lo´pez, and G. James, Modelling DNA at the mesoscale: A challenge for nonlinear science?, Nonlinearity, vol.21, pp.91-100, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00390029

M. Peyrard, S. Cuesta-lo´pez, and G. James, Nonlinear analysis of the dynamics of DNA breathing, J. Biol. Phys, vol.35, pp.73-89, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00389844

J. Fura and S. Rybicki, Periodic solutions of second order Hamiltonian systems bifurcating from infinity, Ann. Inst. Henri Poincare´(C) Anal. Non Line´aire, vol.24, issue.3, pp.471-490, 2007.

D. Chen, S. Aubry, and G. P. Tsironis, Breather Mobility in Discrete 4 Nonlinear Lattices, Phys. Rev. Lett, vol.77, pp.4776-4779, 1996.

T. Cretegny and S. Aubry, Spatially inhomogeneous time-periodic propagating waves in anharmonic systems, Phys. Rev. B, vol.55, pp.11929-11932, 1997.

A. M. Morgante, M. Johansson, S. Aubry, and G. Kopidakis, Breather-phonon resonances in finite-size lattices: 'Phantom breathers'?, J. Phys. A: Math. Gen, vol.35, pp.1-23, 2002.

S. Aubry and G. Abramovici, Chaotic trajectories in the standard map, The concept of antiintegrability, Phys. D, vol.43, pp.199-219, 1990.

S. Aubry, Anti-integrability in dynamical and variational problems, Physica D, vol.86, pp.284-296, 1995.

P. G. Ciarlet, Discrete maximum principle for finite-difference operators, Aequationes Math, vol.4, pp.338-352, 1970.

V. I. Arnold, Ordinary Differential Equations, 1992.

T. Kato, Perturbation Theory for Linear Operators, 1980.

C. Chicone, Ordinary Differential Equations with Applications, vol.34, 1999.

J. L. Mar?´n and S. Aubry, Breathers in nonlinear lattices: Numerical calculation from the anticontinuous limit, Nonlinearity, vol.9, pp.1501-1528, 1996.

J. E. Dennis and R. B. Schnabel, Numerical methods for unconstrained optimization and nonlinear equations, Classics in Applied Mathematics, vol.16, 1996.