Topological instability along invariant surfaces and pseudochaotic transport

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 72, Issue 2, 2005, Pages

  Zaslavsky, G M ^a,b   Carreras, B A ^c   Lynch, V E ^c   Garcia, L ^d   Edelman, M ^a  

^a NEW YORK UNIVERSITY   (United States)

^b POLYTECHNIC UNIVERSITY   (United States)

^c OAK RIDGE NATIONAL LABORATORY   (United States)

^d UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ANOMALOUS TRANSPORT; INVARIANT SURFACES; PSEUDOCHAOTIC TRANSPORT; QUASISTATIONARY;

COMPUTER SIMULATION; LYAPUNOV METHODS; MAGNETIC FIELD EFFECTS; PLASMAS; TOPOLOGY; TRAJECTORIES;

TOKAMAK DEVICES;

EID: 27244443069     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.026227     Document Type: Article

References (42)

1. G. M. Zaslavsky and M. Edelman, Chaos CHAOEH 1054-1500 10.1063/1.1355358 11, 295 (2001).
2. B. A. Carreras, V. E. Lynch, L. Garcia, M. Edelman, and G. M. Zaslavsky, Chaos CHAOEH 1054-1500 10.1063/1.1606611 13, 1175 (2003).
3. I. E. Tamm, Fundamentals of the Theory of Electricity (Gostekhizdat, Moscow, 1946) (in Russian).
4. A. D. Sakharov, Memoirs (A. Knopf, New York, 1990), Chap..
5. S. M. Ulam, A Collection of Mathematical Problems (Interscience, London, 1960), p. 107.
6. V. I. Arnold, Russ. Math. Surveys RMSUAF 0036-0279 18, 85 (1963).
7. V. K. Melnikov, Dokl. Akad. Nauk SSSR DANKAS 0002-3264 148, 1257 (1963).
8. J. K. Moser, Mem. Am. Math. Soc. MAMCAU 0065-9266 81, 1 (1968).
9. G. M. Zaslavsky, R. Z. Sagdeev, D. A. Usikov, and A. A. Chernikov, Weak Chaos and Quasiregular Patterns (Cambridge University Press, Cambridge, U.K., 1991).
10. M. N. Rosenbluth, R. Z. Sagdeev, J. B. Taylor, and G. M. Zaslavsky, Nucl. Fusion NUFUAU 0029-5515 6, 297 (1966).
11. N. N. Filonenko, R. Z. Sagdeev, and G. M. Zaslavsky, Nucl. Fusion NUFUAU 0029-5515 7, 253 (1967).
12. V. I. Arnold, C.R. Hebd. Seances Acad. Sci. COREAF 0001-4036 261, 17 (1965).
13. M. Henon, C.R. Seances Acad. Sci., Ser. A CHASAP 0366-6034 262, 312 (1966).
14. H. Aref, J. Fluid Mech. JFLSA7 0022-1120 143, 1 (1984).
15. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer, Berlin, 1978).
16. V. V. Kozlov, Dokl. Akad. Nauk SSSR DANKAS 0002-3264 249, 1299 (1979).
17. V. V. Kozlov, Symmetries, Topology, and Resonances in Hamiltonian Mechanics (Springer, Berlin, 1996).
18. V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics (Springer, Berlin, 1987).
19. P. J. Richens and M. V. Berry, Physica D PDNPDT 0167-2789 10.1016/0167-2789(81)90024-5 2, 495 (1981).
20. G. M. Zaslavsky and M. Edelman, in Perspective and Problems in Nonlinear Science, edited by, E. Kaplan, J. E. Marsden, and, K. R. Sreenivasan, (Springer, New York, 2003), p. 421;
21. G. M. Zaslavsky and M. Edelman, Physica D PDNPDT 0167-2789 10.1016/j.physd.2004.01.014 193, 128 (2004).
22. G. M. Zaslavsky and M. Edelman, Physica D PDNPDT 0167-2789 10.1016/j.physd.2004.01.014 193, 128 (2004).
23. V. Afraimovich and G. M. Zaslavsky, in Chaos, Kinetics, and Nonlinear Dynamics in Fluids and Plasmas, edited by, S. Benkadda, and, G. M. Zaslavsky, (Springer, Berlin, 1998), p. 59.
24. G. M. Zaslavsky, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(02)00331- 9 371, 461 (2002).
25. E. Gutkin, Ergod. Theory Dyn. Syst. 0143-3857 4, 569 (1984).
26. E. Gutkin and N. Haydn, Ergod. Theory Dyn. Syst. 0143-3857 10.1017/S0143385797088044 17, 849 (1997).
27. E. Gutkin, J. Stat. Phys. JSTPBS 0022-4715 83, 7 (1996).
28. E. Gutkin and A. Katok, in Holomorphic Dynamics, Lecture Notes in Mathematics Vol. 1345 (Springer, Berlin, 1989), p. 163.
29. I. P. Cornfeld S. V. Fomin, and Ya. G. Sinai, Ergodic Theory (Springer, New York, 1982).
30. J. P. Freidberg, Ideal Magnetohydrodynamics (Plenum, New York, 1987).
31. H. P. Furth, M. N. Rosenbluth, and J. Killeen, Phys. Fluids PFLDAS 0031-9171 10.1063/1.1706761 6, 459 (1963).
32. H. Strauss, Phys. Fluids PFLDAS 0031-9171 10.1063/1.862018 20, 1354 (1977).
33. L. Garcia, B. A. Carreras, and V. E. Lynch, Phys. Plasmas PHPAEN 1070-664X 10.1063/1.1430252 9, 47 (2002).
34. B. A. Carreras, P. H. Diamond, M. Murakami, J. L. Dunlap, J. D. Bell, H. R. Hicks, J. A. Holmes, E. A. Lazarus, V. K. Pare, P. Similon, C. E. Thomas, and R. M. Wieland, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.50.503 50, 503 (1983).
35. P. Beyer, S. Benkadda, X. Garbet, and P. H. Diamond, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.4892 85, 4892 (2000).
36. R. Bowen, Trans. Am. Math. Soc. TAMTAM 0002-9947 184, 125 (1973).
37. V. Afraimovich and G. M. Zaslavsky, Chaos CHAOEH 1054-1500 10.1063/1.1566171 13, 519 (2003).
38. G. M. Zaslavsky and M. Edelman (unpublished).
39. A. Ya. Khinchin, Continued Fractions (University of Chicago Press, Chicago, 1964).
40. Th. Niemeijer and J. M. J. van Leeuwen, in Phase Transition and Critical Phenomena, edited by, C. Domb, and, M. S. Green, (Academic Press, London, 1976), Vol. 6, p. 425.
41. B. D. Hughes, M. F. Shlesinger, and E. W. Montroll, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 78, 3287 (1981).
42. E. W. Weisstein, http://mathworld.wolfram.com/KhinchinsConstant.html