Geometric amplitude, adiabatic invariants, quantization, and strong stability of Hamiltonian systems

Journal of Mathematical Physics

Volumn 43, Issue 1, 2002, Pages 25-42

  Bliokh, K Yu ^a  

^a INSTITUTE OF RADIO ASTRONOMY   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035981931     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1418718     Document Type: Article

References (23)

1. M.V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984).
2. M.V. Berry, J. Phys. A 18, 15 (1985).
3. J.H. Hannay, J. Phys. A 18, 221 (1985).
4. S.I. Vinitskiy, V.L. Debrov, V.M. Dubovik, B.L. Markovski, and Yu.P. Stepanovskiy, Geometric Phases in Physics, edited by A. Shapere and F. Wilczek (World Scientific, Singapore, 1989). S.I. Vinitskiy, V.L. Debrov, V.M. Dubovik, B.L. Markovski and Yu.P. Stepanovskiy, Usp. Fiz. Nauk 160, 6 (1990).
5. S.I. Vinitskiy, V.L. Debrov, V.M. Dubovik, B.L. Markovski, and Yu.P. Stepanovskiy, Geometric Phases in Physics, edited by A. Shapere and F. Wilczek (World Scientific, Singapore, 1989). S.I. Vinitskiy, V.L. Debrov, V.M. Dubovik, B.L. Markovski and Yu.P. Stepanovskiy, Usp. Fiz. Nauk 160, 6 (1990).
6. J.C. Garrison and E.M. Wright, Phys. Lett. A 128, 177 (1988).
7. Y.C. Ge and M.S. Child, Phys. Rev. A 58, 872 (1998).
8. K. Yu. Bliokh, J. Phys. A 32, 2551 (1999).
9. W. Wasow, Asymptotic Expansions for Ordinary Differential Equations (Wiley, New York, 1965).
10. V.I. Arnold, Selecta Math., New Ser. 1, 1 (1995).
11. M.V. Berry and K.E. Mount, Rep. Prog. Phys. 35, 315 (1972).
12. E. Cartan, Lecons Sur Les Invariants Integraux (Hermann, Paris, 1922).
13. A.S. Bakai and Yu.P. Stepanovskiy, Adiabatic Invariants (Naukova Dumka, Kiev, 1981).
14. V.A. Yakubovich and V.M. Starzhinskiy, Linear Differential Equations With Periodic Coefficient (Nauka, Moskow, 1972).
15. V.I. Arnold, Mathematical Methods in Classical Mechanics (Springer-Verlag New York, 1978). Geometrical Methods in the Theory of Ordinary Differential Equations (Springer-Verlag, New York, 1983).
16. V.I. Arnold, Mathematical Methods in Classical Mechanics (Springer-Verlag New York, 1978). Geometrical Methods in the Theory of Ordinary Differential Equations (Springer-Verlag, New York, 1983).
17. P.A.M. Dirac, The Principles of Quantum Mechanics (Clarendon, Oxford, 1958).
18. P. Ehrenfest, Proc. Amsterdam Acad. 16, 591 (1913); P. Ehrenfest, Naturwissenschaften 11, 543 (1923).
19. P. Ehrenfest, Proc. Amsterdam Acad. 16, 591 (1913); P. Ehrenfest, Naturwissenschaften 11, 543 (1923).
20. V.A. Fok, Proc. LGU 16, 67 (1959).
21. G.D. Birkhoff, Dynamical Systems, American Mathematic Society Colloquium Publication, 1927, Vol. 9.
22. G. Sardanashvili, J. Math. Phys. 41, 5245 (2000).
23. J.L. Massera and J.J. Schaffer, Linear Differential Equations and Function Spaces (Academic, New York 1966).