Geodesic
Resonant phenomena in slowly irregular rectangular waveguides
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 173-179 
A. P. Itin; A. I. Neishtadt; A. A. Vasil'ev. Resonant phenomena in slowly irregular rectangular waveguides. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 173-179. http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a15/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The waveguide with a rectangular cross section of size and orientation slowly changing along the waveguide's length is considered. Methods of the canonical perturbation theory to describe the ray dynamics in the waveguide are used. As the size and orientation of cross section slowly changes along the ray trajectory, certain resonance conditions can be satisfied. The phenomena of scattering on a resonance and capture into a resonance is studied. These phenomena lead to destruction of adiabatic invariance in the system.

[1] V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer, New York, 1978 | MR

[2] R. Z. Sagdeev, D. A. Usikov, G. M. Zaslavsky, Nonlinear Physics, Harwood Academic Publishers, Chur, 1988

[3] A. D. Shatrov, Izv. VUZov, “Radiophysica”, 20:8 (1977), 1153

[4] V. A. Borovikov, A. V. Popov,, Direct and Inverse Problems of Theory of Diffraction, IRE, Moscow, 1979

[5] A. I. Neishtadt, “Propagation of beams through smoothly irregular waveguides and theory of perturbations in Hamiltonian systems”, Izv. VUZov, “Radiophysica”, 25:2 (1982), 218–226 | MR

[6] Yu. A. Kravtsov, Yu. A. Orlov, Geometrical Optics Of Inhomogeneous Media, Springer-Verlag, New York, 1990 | MR | Zbl

[7] L. M. Brekhovskikh, O. A. Godin, Acoustics of Layered Media II - Point Sources and Bounded Beams, Springer-Verlag, Berlin, Heidelberg, New York, 1999

[8] A. I. Neishtadt, “On adiabatic invariance in two-frequency systems”, Hamiltonian Systems with Three or More Degrees of Freedom, NATO ASI Series C, 533, eds. C. Simo, Kluwer Academic Publishers, Dordrecht, 1999, 193–213 | MR

[9] A. P. Itin, A. I. Neishtadt, A. A. Vasiliev, “Resonant phenomena in slowly perturbed rectangular billiards”, Phys. Lett. A, 291 (2001), 133–138 | DOI | Zbl

[10] A. P. Itin, A. I. Neishtadt, “Resonant phenomena in slowly perturbed elliptic billiards”, Regular and Chaotic Dynamics, 2 (2003) (to appear) | MR

[11] V. I. Arnold, V. V. Kozlov, A. I. Neishtadt, Mathematical aspects of classical and celestial mechanics, Encyclopaedia of Mathematical Sciences, 3, Springer, Berlin, 1988

[12] A. P. Itin, A. I. Neishtadt, A. A. Vasiliev, “Captures into resonance and scattering on resonance in dynamics of a charged relativistic particle in magnetic field and electrostatic wave”, Physica D, 141 (2000), 281–296 | DOI | MR | Zbl