Hidden renormalization group for the near-separatrix Hamiltonian dynamics

Physics Report

Volumn 288, Issue 1-6, 1997, Pages 457-485

  Kuznetsov, L ^a   Zaslavsky, George M ^a,b  

^a POLYTECHNIC UNIVERSITY   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031236892     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(97)00037-9     Document Type: Article

References (55)

1. [1] V.I. Arnold, Mathematical Methods of Classical Mechanics, Springer, New York, 1989.
2. [2] V.K. Melnikov, Dokl. Akad. Nauk 148 (1963) 1257.
3. [3] N.N. Filonenko, R.Z. Sagdeev, G.M. Zaslavsky, Nucl. Fusion 7 (1965) 253.
4. [4] N.N. Filonenko, G.M. Zaslavsky, Sov. Phys. JETP 25 (1968) 851.
5. [5] B.V. Chirikov, Phys. Rep. 52 (1979) 264.
6. [6] S. Wiggins, Chaotic Transport in Dynamical Systems, Springer, New York, 1992.
7. [7] V. Rom-Kedar, A. Leonard, S. Wiggins, J. Fluid Mech. 214 (1990) 347.
8. [8] C. Amick, E.S.C. Ching, L.P. Kadanoff, V. Rom-Kedar, J. Nonlinear Sci. 2 (1992) 9; V. Rom-Kedar, L.P. Kadanoff, E.S.C. Ching, C. Amick, Physica D 62 (1993) 51.
9. [8] C. Amick, E.S.C. Ching, L.P. Kadanoff, V. Rom-Kedar, J. Nonlinear Sci. 2 (1992) 9; V. Rom-Kedar, L.P. Kadanoff, E.S.C. Ching, C. Amick, Physica D 62 (1993) 51.
10. [9] V.F. Lazutkin, I.G. Schachmanski, M.B. Tabanov, Physica D 40 (1989) 235; Sov. Math. Dokl. 42 (1991) 5; V.G. Gelfreich, V.F. Lazutkin, M.B. Tabanov, Chaos 1 (1991) 137.
11. [9] V.F. Lazutkin, I.G. Schachmanski, M.B. Tabanov, Physica D 40 (1989) 235; Sov. Math. Dokl. 42 (1991) 5; V.G. Gelfreich, V.F. Lazutkin, M.B. Tabanov, Chaos 1 (1991) 137.
12. [9] V.F. Lazutkin, I.G. Schachmanski, M.B. Tabanov, Physica D 40 (1989) 235; Sov. Math. Dokl. 42 (1991) 5; V.G. Gelfreich, V.F. Lazutkin, M.B. Tabanov, Chaos 1 (1991) 137.
13. [10] G.M. Zaslavsky, R.Z. Sagdeev, D.A. Usikov, A.A. Chernikov, Weak Chaos and Quasiregular Patterns, Cambridge Univ. Press, Cambridge, 1991.
14. [11] D.V. Treshchev, Chaos 6 (1996) 6.
15. [12] D. Escande, Phys. Rep. 121 (1985) 163.
16. [13] V.V. Afanasiev, A.A. Chernikov, R.Z. Sagdeev, G.M. Zaslavsky, Phys. Lett. A 144 (1990) 229.
17. [14] V. Rom-Kedar, Nonlineariry 7 (1994) 441; Chaos 5 (1995) 385.
18. [14] V. Rom-Kedar, Nonlineariry 7 (1994) 441; Chaos 5 (1995) 385.
19. [15] S. Pekarsky, V. Rom-Kedar, unpublished 1996.
20. [16] G.M. Zaslavsky, Chaos 4 (1994) 589.
21. [17] B.V. Chirikov, D.L. Shepeliansky, Physica D 13 (1984) 394.
22. [18] B.V. Chirikov, Chaos Solitons Fractals 1 (1991) 79.
23. [19] G.M. Zaslavsky, S.S. Abdullaev, Phys. Rev. E 51 (1995) 3901.
24. [20] S.S. Abdullaev, G.M. Zaslavsky, Phys. Plasmas 2 (1995) 4533; 3 (1996) 516.
25. [20] S.S. Abdullaev, G.M. Zaslavsky, Phys. Plasmas 2 (1995) 4533; 3 (1996) 516.
26. [21] J. Meiss, Phys. Rev. A 34 (1986) 2375; Rev. Mod. Phys. 64 (1992) 795.
27. [21] J. Meiss, Phys. Rev. A 34 (1986) 2375; Rev. Mod. Phys. 64 (1992) 795.
28. [22] V.K. Melnikov, unpublished 1996.
29. [23] G.M. Zaslavsky, M. Edelman, B. Niyazov, Chaos (1997) to appear.
30. [24] A. Delshams, T.M. Seara, Commun. Math. Phys. 150 (1992) 433.
31. [25] A. Lichtenberg, M. Lieberman, Regular and Stochastic Motion, Springer, New York, 1983.
32. [26] J.E. Marsden, T.S. Ratiu, Introduction to Mechanics and Symmetry, Springer, New York, 1994.
33. [27] I.G. Sinai, Topics in Ergodic Theory, Princeton Univ. Press, Princeton, 1994.
34. [28] G.M. Zaslavsky, Chaos in Dynamical Systems, Harwood Acad. Publ., New York, 1985.
35. [29] S.G. Matinyan, G.K. Savvidi, Nucl. Phys. B 134 (1978) 539.
36. [30] S.G. Matinyan, G.K. Savvidi, N.G. Ter-Arutunyan-Savvidi, JETP Lett. 34 (1981) 65.
37. [31] S.G. Matinyan, G.K. Savvidi, N.G. Ter-Arutunyan-Savvidi, JETP 53 (1981) 421.
38. [32] B.V. Chirikov, D.L. Shepeliansky, Sov. J. Nucl. Phys. 36 (1982) 908.
39. [33] T.H. Seligman, J.J.M. Verbaarschot, M.R. Zirnbauer, J. Phys. A 18 (1985) 2751; Phys. Rev. Lett. 53 (1984).
40. [33] T.H. Seligman, J.J.M. Verbaarschot, M.R. Zirnbauer, J. Phys. A 18 (1985) 2751; Phys. Rev. Lett. 53 (1984).
41. [34] R.A. Pullen, A.R. Edmonds, J. Phys. A 14 (1981) L477.
42. [35] S. Chang, Phys. Rev. D 29 (1984) 259.
43. [36] A. Carnegie, I.C. Percival, J. Phys. A 17 (1984) 801.
44. [37] E. Haller, H. Köppel, L.S. Cederbaum, J. Phys. A 17 (1984) L831.
45. [38] M. Lakshmanan, R. Sahadevan, Phys. Rev. A 31 (1985) 861.
46. [39] E. Caurier, B. Grammaticos, Europhys. Lett. 2 (1986) 417.
47. [40] E.B. Bogomol'nyǐ, JETP Lett. 41 (1985) 65.
48. [41] Th. Zimmermann, H.-D. Meyer, H. Köppel, L.S. Cederbaum, Phys. Rev. A 33 (1986) 4334.
49. [42] P.A. Vorob'ev, G.M. Zaslavsky, Sov. Phys. JETP 65 (5) (1987) 877.
50. [43] R.L. Waterland, J.M. Yuan, C.C. Martens, R.E. Gillian, W.P. Reinhardt, Phys. Rev. Lett. 61 (1988) 2733.
51. [44] O. Bohigas, S. Tomsovic, D. Ullmo, Phys. Rep. 223 (1993) 43.
52. [45] T.S. Biró, S.G. Matinyan, B. Müller, Chaos and Gauge Field Theory, World Scientific, Singapore, 1994.
53. [46] R. McLachlan, P. Atela, Nonlinearity 5 (1992) 541.
54. [47] E. Forest, R. Ruth, Physica D 43 (1990) 105.
55. [48] F. Kang, Q. Meng-Zhao, in: Z. You-lan, G. Ben-yu (Eds.), Numerical Methods for PDE, Lecture Notes in Mathematics, vol. 1297, Springer, New York, 1987, p. 1.