Integrability and ergodicity of classical billiards in a magnetic field

Journal of Statistical Physics

Volumn 83, Issue 1-2, 1996, Pages 81-126

  Berglund, N ^a   Kunz, H ^a  

^a EPFL   (Switzerland)

Author keywords

Adiabatic invariant; Billiards; Ergodicity; Integrability; Magnetic field; Twist map

Indexed keywords

EID: 0030536725     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02183641     Document Type: Article

References (16)

1. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer, Berlin, 1978, 1989).
2. V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations (Springer, Berlin, 1983).
3. G. D. Birkhoff, Dynamical Systems (American Mathematical Society, Providence, Rhode Island, 1927, 1966).
4. R. Douady, Applications du théorème des tores invariants, Thèse 3ème cycle, Université Paris VII (1982).
5. T. Dagaeff and C. Rouvinez, On the discontinuities of the boundary in billiards, Physica D 67:166-187 (1993).
6. A. Hubacher, Instability of the boundary in the billiard ball problem, Commun. Math. Phys. 108:483-488 (1987).
7. V. V. Kozlov and D. V. Treshchev, Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts (American Mathematical Society, Providence, Rhode Island, 1991).
8. V. F. Lazutkin, The existence of caustics for a billiard ball problem in a convex domain, Math. USSR Izv. 7:185-214 (1973).
9. L. P. Lévy, D. H. Reich, L. Pfeiffer, and K. West, Aharonov-Bohm ballistic billiards, Physica B 189:204 (1993).
10. J. N. Mather, Glancing billiards, Ergod. Theory Dynam. Syst. 2:397-403 (1982).
11. J. D. Meiss, Symplectic maps, variational principles, and transport, Rev. Mod. Phys. 64:795-848 (1992).
12. J. Moser, Stable and Random Motions in Dynamical Systems ( Princeton University Press, Princeton, New Jersey, 1973).
13. O. Meplan, F. Brut, and C. Gignoux. Tangent map for classical billiards in magnetic fields, J. Phys. A 26:237-246 (1993).
14. M. Robnik, Regular and chaotic billiard dynamics in magnetic fields, in Nonlinear Phenomena and Chaos, S. Sakar, ed. (Adam Hilger, Bristol, 1986), pp. 303-330.
15. M. Robnik and M. V. Berry, Classical billiards in magnetic fields, J. Phys. A 18:1361-1378 (1985).
16. K. Rezakhanlou, H. Kunz, and A. Crisanti, Stochastic behaviour of the magnetisation in a classically integrable quantum system, Europhys. Lett. 16:629-634 (1991).