A Nekhoroshev-type theorem for the Pauli-Fierz model of classical electrodynamics
Annales de l'I.H.P. Physique théorique, Tome 60 (1994) no. 3, pp. 339-371. 
@article{AIHPA_1994__60_3_339_0,
     author = {Bambusi, Dario},
     title = {A {Nekhoroshev-type} theorem for the {Pauli-Fierz} model of classical electrodynamics},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {339--371},
     publisher = {Gauthier-Villars},
     volume = {60},
     number = {3},
     year = {1994},
     mrnumber = {1281651},
     zbl = {0805.35130},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1994__60_3_339_0/}
}
TY  - JOUR
AU  - Bambusi, Dario
TI  - A Nekhoroshev-type theorem for the Pauli-Fierz model of classical electrodynamics
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1994
SP  - 339
EP  - 371
VL  - 60
IS  - 3
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPA_1994__60_3_339_0/
LA  - en
ID  - AIHPA_1994__60_3_339_0
ER  - 
%0 Journal Article
%A Bambusi, Dario
%T A Nekhoroshev-type theorem for the Pauli-Fierz model of classical electrodynamics
%J Annales de l'I.H.P. Physique théorique
%D 1994
%P 339-371
%V 60
%N 3
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPA_1994__60_3_339_0/
%G en
%F AIHPA_1994__60_3_339_0
Bambusi, Dario. A Nekhoroshev-type theorem for the Pauli-Fierz model of classical electrodynamics. Annales de l'I.H.P. Physique théorique, Tome 60 (1994) no. 3, pp. 339-371. http://archive.numdam.org/item/AIHPA_1994__60_3_339_0/

[1] D. Bambusi and L. Galgani, Some Rigorous Results on the Pauli-Fierz Model of Classical Electrodynamics, Ann. Inst. H. Poincaré, Physique théorique, Vol. 58, 1993, pp. 155-171. | Numdam | MR | Zbl

[2] L. Galgani, C. Angaroni, L. Forti, A. Giorgilli and F. Guerra, Classical Electrodynamics as a Nonlinear Dynamical System, Phys. Lett. A, Vol. 139, 1989, pp. 221-230.

[3] W. Pauli and M. Fierz, Zur Theorie der Emission langwelliger Lichtquanten, Nuovo Cimento, Vol. 15, 1938, pp. 167-188. | JFM

[4] M. Abraham, Prinzipien der Dynamik des Elektrons, Ann. der Phys., Vol. 10, 1903, pp. 105-179. | JFM

[5] M. Abraham, Theorie der Elektrizität, Vol. II, Tebeuner, Leipzig-Berlin 1908. | JFM

[6] A. Einstein, Zum gegenwärtigen Stand des Strahlungsproblems, Phys. Zeit., Vol. 6, 1909, pp. 185-186. | JFM

[7] L. Landau and E. Lifchitz, Théorie des champs, 3rd Ed., MIR, Moscow, 1970.

[8] J.D. Jackson, Classical Electrodynamics, John Wiley & Sons, New York, 1975. | Zbl

[9] G.A. Schott, The Electromagnetic Field of a Moving Uniformly and Rigidly Electrified Sphere and its Radiationless Orbits, Phyl. Mag., Vol. 15, 1933, pp. 752-761. | Zbl

[10] D. Bohm and M. Weinstein, The Self Oscillations of a Charged Particle, Phys. Rev., Vol. 74, 1948, pp. 1789-1798. | Zbl

[11] W.T. Grandy and A. Aghazadeh, Radiative Corrections for Extended Charged Particles in Classical Electrodynamics, Ann. of Physics, Vol. 142, 1982, pp. 284-298. | MR

[12] E. Zehnder, Siegel Linearization Theorem in Infinite Dimension, Manuscripta Math., Vol. 23, 1978, pp. 363-371. | MR | Zbl

[13] N.V. Nikolenko, The Method of Poincaré Normal Form in Problems of Integrability of Equations of Evolution Type, Uspekhi Mat. Nauk., Vol. 41, 5, 1986, pp. 109-152; Russ. Math. Surveys, Vol. 41, 5, 1986, pp. 63-114. | MR | Zbl

[14] J. Fröhlich, T. Spencer and C.E. Wayne, Localization in Disordered, Nonlinear Dynamical Systems, J. Stat. Phys., Vol. 42, 1986, pp. 247-274. | MR | Zbl

[15] M. Vittot and J. Bellissard, Invariant Tori for an Infinite Lattice of Coupled Classical Rotators, Preprint, 1985.

[16] S.B. Kuksin, Hamiltonian Perturbations of Infinite-dimensional Linear Systems with Imaginary Spectrum, Funktsional. Anal. i Prilozhen, Vol. 21, 3, 1987, pp. 22-37; Funct. Anal. Appl., Vol. 21, 1987. | MR | Zbl

[17] C.E. Wayne, Periodic and Quasi-periodic Solutions of Nonlinear Wave Equation via KAM Theory, Commun. Math. Phys., Vol. 127, 1990, pp. 479-528. | MR | Zbl

[18] J. Pöschel, Small Divisors with Spatial Structure in Infinite Dimensional Hamiltonian Systems, Commun. Math. Phys., Vol. 127, 1990, pp. 351-393. | MR | Zbl

[19] M. Yu. DENISOV, Reduction of the Nonlinear Diffusion Equation to Linear Form, Funktional. Anal. i Prilozhen, Vol. 19, 1, 1985, pp. 69-70; Function. Anal. Appl., Vol. 19, 1985, pp. 57-58. | MR | Zbl

[20] M. Yu. Denisov, Reduction of some Nonlinear Evolution Equation with Continuous Spectrum to Linear Part, Differentsial'nye Uravneniya, Vol. 21, 1985, pp. 464-473; Differential equations, Vol. 21, 1985, pp. 312-319. | MR | Zbl

[21] G. Benettin, J. Fröhlich and A. Giorgilli, A Nekhoroshev-type Theorem for Hamiltonian Systems with Infinitely Many Degrees of Freedom, Commun. Math. Phys., Vol. 119, 1988, pp. 95-108. | MR | Zbl

[22] S.B. Kuksin, An Averaging Theorem for Distributed Conservative Systems and its Application to Von Karman's Equation, PMM U.S.S.R., Vol. 53, 1989, pp. 150-157. | MR | Zbl

[23] D. Bambusi and A. Giorgilli, Exponential stability of states close to resonance in infinite dimensional hamiltonian systems, Jour. Stat. Phys., Vol. 71, 1993. | MR | Zbl

[24] G. Benettin, L. Galgani and A. Giorgilli, Realization of Holonomic Constraints and Freezing of High Frequency Degrees of Freedom in the Light of Classical Perturbation Theory, Part II, Commun. Math. Phys., Vol. 121, 1989, pp. 557-601. | MR | Zbl

[25] J.-L. Lions, Problèmes aux Limites, Presses de l'Université de Montréal, 1962.

[26] R. Dautray and J.-L. Lions, Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, Masson, Paris, 1985. | Zbl

[27] M. Born, Ann. d. Phys., Vol. 30, 1, 1909. | JFM

[28] J.S. Nodvik, A covariant Formulation of Classical Electrodynamics for Charges of Finite Extension, Ann. of Phys., Vol. 28, 1964, pp. 225-319. | MR | Zbl

[29] A. Giorgilli and L. Galgani, Formal Integrals for an Autonomous Hamiltonian System Near an Equilibrium Point, Cel. Mech., Vol. 17, 1978, pp. 267-280. | MR | Zbl

[30] J. Mujica, Complex Analysis in Banach Spaces, North Holland Mathematical Studies 120, Amsterdam, 1986. | MR | Zbl