Scaling invariance of the homoclinic tangle

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 4, 2002, Pages 7-

  Kuznetsov, L ^a   Zaslavsky, G M ^b  

^a BROWN UNIVERSITY   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC LAYER; MAGNETIC SURFACES; PARAMETER CONTROL; SPIN ORBITS;

BOUNDARY CONDITIONS; DEGREES OF FREEDOM (MECHANICS); EQUATIONS OF MOTION; FLUID MECHANICS; PERTURBATION TECHNIQUES; SURFACE PHENOMENA; TOPOLOGY;

HAMILTONIANS;

ARTICLE;

EID: 37649026517     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.046212     Document Type: Article

References (43)

1. H. Aref, J. Fluid Mech. 143, 1 (1984).
2. H. Aref, Philos. Trans. R. Soc. London, Ser. A 333, 273 (1990).
3. D. DelCastillo-Negrete, Phys. Fluids 10, 576 (1998).
4. J. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport (Cambridge University Press, Cambridge, 1989).
5. K. Ngan and T. Shepherd, J. Fluid Mech. 334, 315 (1997).
6. J. Weiss and E. Knobloch, Phys. Rev. A 40, 2579 (1989).
7. G.M. Zaslavsky, Fluid Dyn. Res. 8, 127 (1991).
8. N.N. Filonenko and G.M. Zaslavsky [Sov. Phys. JETP 25, 851 (1968)].
9. A. Punjabi, A. Verma, and A. Boozer, J. Plasma Phys. 52, 91 (1994).
10. A. Iomin, D. Gangardt, and S. Fishman, Phys. Rev. E 57, 4054 (1998).
11. D. Rakhlin, Phys. Rev. E 63, 011112 (2000).
12. R. Malhotra, M. Holman, and T. Ito, Proc. Natl. Acad. Sci. U.S.A. 98, 12342 (2001).
13. I. Shevchenko, Phys. Scr. 57, 185 (1998).
14. C. Karney, Physica D 8, 360 (1983).
15. J. Hanson, J. Cary, and J. Meiss, J. Stat. Phys. 39, 327 (1985).
16. R. MacKay, J. Meiss, and I. Percival, Physica D 13, 329 (1984).
17. J. Meiss and E. Ott, Physica D 20, 387 (1986).
18. T.H. Solomon, E.R. Weeks, and H.L. Swinney, Physica D 76, 70 (1994).
19. V. Afraimovich and G. Zaslavsky, Phys. Rev. E 55, 5418 (1997).
20. L. Kuznetsov and G. Zaslavsky, Phys. Rev. E 61, 3777 (2000).
21. G. Zaslavsky, D. Stevens, and H. Weitzner, Phys. Rev. E 48, 1683 (1993).
22. G. Zaslavsky and M. Edelman, Chaos 10, 135 (2000).
23. V. Rom-Kedar, A. Leonard, and S. Wiggins, J. Fluid Mech. 214, 347 (1990).
24. V. Rom-Kedar and A. Poje, Phys. Fluids 11, 2044 (1999).
25. V. Rom-Kedar and G. Zaslavsky, Chaos 9, 697 (1999).
26. V. Melnikov, Trans. Mosc. Math. Soc. 12, 1 (1963).
27. B. Chirikov, Phys. Rep. 52, 263 (1979).
28. V. Rom-Kedar, Nonlinearity 7, 441 (1994).
29. D. Treschev, Physica D 116, 21 (1998).
30. G. Zaslavsky and S. Abdullaev, Phys. Rev. E 51, 3901 (1995).
31. S. Abdullaev and G. Zaslavsky, Phys. Plasmas 3, 516 (1996).
32. L. Kuznetsov and G. Zaslavsky, Phys. Rep. 288, 457 (1997).
33. S.S. Abdullaev and K. Spatschek, Phys. Rev. E 60, 6287 (1999).
34. S.S. Abdullaev, Phys. Rev. E 62, 3508 (2000).
35. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
36. H. Nusse and J. Yorke, Dynamics: Numerical Explorations (Springer-Verlag, New York, 1998).
37. R. McLachlan and P. Atela, Nonlinearity 5, 541 (1991).
38. G. Zaslavsky, R. Sagdeev, D. Usikov, and A. Chernikov, Weak Chaos and Quasiregular Patterns (Cambridge University Press, Cambridge, England, 1991).
39. T. Ahn, G. Kim, and S. Kim, Physica D 89, 315 (1996).
40. S. Abdullaev and G. Zaslavsky, Phys. Plasmas 2, 4533 (1995).
41. I. Shevchenko, J. Exp. Theor. Phys. 91, 615 (2000).
42. A. Luo and R. Han, Chaos, Solitons Fratals 12, 2493 (2001).
43. A.J. Lichtenberg and M.A. Lieberman, Regular and Chaotic Dynamics (Springer-Verlag, New York, 1992).