Derivatives and constraints in chaotic flows: Asymptotic behaviour and a numerical method

Physica D: Nonlinear Phenomena

Volumn 172, Issue 1-4, 2002, Pages 139-161

  Thiffeault, Jean Luc ^a  

^a Department of Earth and Environmental Sciences   (United States)

Author keywords

Chaotic flows; Lagrangian coordinates; Lyapunov exponents

Indexed keywords

ASYMPTOTIC STABILITY; CONSTRAINT THEORY; LAGRANGE MULTIPLIERS; LYAPUNOV METHODS; PERTURBATION TECHNIQUES;

CHAOTIC FLOWS;

CHAOS THEORY;

EID: 0037112341     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(02)00588-2     Document Type: Article

References (39)

1. J. Guckenheimer, P.J. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York, 1983.
2. V.I. Arnold, Ordinary Differential Equations, 3rd Edition, Springer, Berlin, 1992.
3. Eckmann J.-P., Ruelle D., Rev. Mod. Phys. 57 1985 617.
4. A.M. Lyapunov, The General Problem of the Stability of Motion, Taylor & Francis, London, 1992 (Engl. Transl.). First Published in Russian in 1892 by the Mathematical Society of Kharkov.
5. Boozer A.H., Astrophys. J. 394 1992 357.
6. Tang X.Z., Boozer A.H., Physica D 95 1996 283.
7. Tang X.Z., Boozer A.H., Phys. Plasmas 7 2000 1113.
8. Giona M., Adrover A., Phys. Rev. Lett. 81 1998 3864.
9. Adrover A., Giona M., Phys. Rev. E 60 1999 347.
10. L.D. Landau, E.M. Lifschitz, Fluid Mechanics, Course of Theoretical Physics, Vol. 6, 2nd Edition, Butterworths/Heinemann, Oxford, UK, 1998.
11. S. Childress, A.D. Gilbert, Stretch, Twist, Fold: The Fast Dynamo, Springer, Berlin, 1995.
12. J.-L. Thiffeault, Preprint, 2001. nlin.CD/0105026 .
13. Dressler U., Farmer J.D., Physica D 59 1992 365.
14. Taylor T.J., Nonlinearity 6 1993 369.
15. Batchelor G.K., Proc. R. Soc. London A 213 1952 349.
16. Pope S.B., Int. J. Eng. Sci. 26 1988 445.
17. Pope S.B., Yeung P.K., Girimaji S.S., Phys. Fluids A 1 1989 2010.
18. Girimaji S.S., Phys. Fluids A 3 1991 1772.
19. Drummond I.T., Münch W., J. Fluid Mech. 225 1991 529.
20. Liu M., Muzzio F.J., Phys. Fluids 8 1996 75.
21. Hobbs D.M., Muzzio F.J., Phys. Fluids 10 1998 1942.
22. Cerbelli S., Zalc J.M., Muzzio F.J., Chem. Eng. Sci. 55 2000 363.
23. Greene J.M., Kim J.S., Physica D 24 1987 213.
24. Goldhirsch I., Sulem P., Orszag S.A., Physica D 27 1987 311.
25. Thiffeault J.-L., Boozer A.H., Chaos 11 2001 16.
26. Geist K., Parlitz U., Lauterborn W., Prog. Theoret. Phys. 83 1990 875.
27. Bennetin G., Galgani L., Strelcyn J.-M., Phys. Rev. A 14 1976 2338.
28. Shimada I., Nagashima T., Prog. Theoret. Phys. 61 1979 1605.
29. J.M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport, Cambridge University Press, Cambridge, UK, 1989.
30. Oseledec V.I., Trans. Moscow Math. Soc. 19 1968 197.
31. Tang X.Z., Boozer A.H., Phys. Fluids 11 1999 1418.
32. Tang X.Z., Boozer A.H., Chaos 9 1999 183.
33. B. Schutz, Differential Geometry, Cambridge University Press, Cambridge, UK, 1980.
34. R.M. Wald, General Relativity, University of Chicago Press, Chicago, IL, 1984.
35. Christiansen F., Rugh H.H., Nonlinearity 10 1997 1063.
36. J.-L. Thiffeault, Preprint, 2002. nlin.CD/0204069 .
37. J.-L. Thiffeault, A.H. Boozer, Preprint, Phys. Plasmas, submitted for publication.
38. Giona M., Adrover A., Muzzio F.J., Cerbelli S., Physica D 132 1999 298.
39. Giona M., Adrover A., Muzzio F.J., Cerbelli S., Chem. Eng. Sci. 55 2000 381.