Variational method for finding periodic orbits in a general flow

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

Volumn 69, Issue 1 2, 2004, Pages 162171-1621710

  Lan, Yueheng ^a   Cvitanović, Predrag ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CHAOS THEORY; COMPUTER SIMULATION; FOURIER TRANSFORMS; HAMILTONIANS; ITERATIVE METHODS; LAGRANGE MULTIPLIERS; ORBITS; PARTIAL DIFFERENTIAL EQUATIONS; PHASE SPACE METHODS; TOPOLOGY; TURBULENCE;

EXTENDED SYSTEMS; NEWTON-RAPHSON METHOD;

VARIATIONAL TECHNIQUES;

EID: 4444284698     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (42)

1. D. Ruelle, Statistical Mechanics, Thermodynamic Formalism (Addison-Wesley, Reading, MA, 1978).
2. M. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
3. R. Artuso, E. Aurell, and P. Cvitanović, Nonlinearity 3, 325 (1990).
4. H. Rugh, Nonlinearity 5, 1237 (1992).
5. P. Cvitanović, R. Artuso, R. Mainieri, G. Tanner, and G. Vattay, Chaos: Classical and Quantum (Niels Bohr Institute, Copenhagen, 2003).
6. F. Diakonos, P. Schmelcher, and O. Biham, Phys. Rev. Lett. 81, 4349 (1998).
7. O. Biham and W. Wenzel, Phys. Rev. Lett. 63, 819 (1989).
8. R. L. Davidchack and Y.-C. Lai, Phys. Rev. E 60, 6172 (1999).
9. D. Viswanath, Nonlinearity 16, 1035 (2003).
10. C. Falcolini and R. de la Llave, J. Stat. Phys. 67, 645 (1992).
11. S. Tompaidis, Exp. Math. 5, 211 (1996).
12. H.-T. Kook and J. D. Meiss, Physica D 36, 317 (1989).
13. D. Pingel, P. Schmelcher, and F. K. Diakonos, Phys. Rev. E 64, 026214 (2001).
14. U. Frisch, Turbulence (Cambridge University Press, Cambridge, England, 1996).
15. I. S. Aranson and L. Kramer, Rev. Mod. Phys. 74, 99 (2002).
16. T. S. Biró, S. G. Matinyan, and B. Müller, Chaos and Gauge Field Theory (World Scientific, Singapore, 1994).
17. P. Cvitanović, Physica A 288, 61 (2000).
18. G. Kawahara and S. Kida, J. Fluid Mech. 449, 291 (2001).
19. P. Cvitanović and Y. Lan, in Proceedings of the 10th International Workshop on Multiparticle Production: Correlations and Fluctuations in QCD, edited by N. Antoniou (World Scientific, Singapore, 2003).
20. F. Christiansen, in Chaos: Classical and Quantum [5], Chap. 14.
21. V. I. Arnol'd, Ordinary Differential Equations (Springer, New York, 1992).
22. H. B. Keller, Numerical Methods for Two-Point Boundary-Value Problems (Dover, New York, 1992).
23. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer, New York, 1983).
24. J. N. Mather, J. Am. Soc. 4, 207 (1991).
25. H.-T. Kook and J. D. Meiss, Physica D 35, 65 (1989).
26. S. B. Angenent, Commun. Math. Phys. 115, 353 (1988).
27. C. Golé, Math. Z. 210, 441 (1992).
28. A. Brandenburg, in Advances in Nonlinear Dynamos, edited by A. Ferriz-Mas and M. Núñez (Taylor & Francis, London, 2003).
29. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, England, 1992).
30. J. W. Thomas, Numerical Partial Differential Equations (Springer, New York, 1995).
31. B. Roždestvenskiǐ and N. Janenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics (American Mathematical Society, Providence, RI, 1983).
32. F. Christiansen, P. Cvitanović, and V. Putkaradze, Nonlinearity 10, 55 (1997).
33. C. Conley, Isolated Invariant Sets and the Morse Index (American Mathematical Society, Providence, RI, 1978).
34. P. Cvitanović and B. Eckhardt, Nonlinearity 6, 277 (1993).
35. M. Hénon, Generating Families in the Restricted Three-Body Problem II. Quantitative Study of Bifurcations (Springer, New York, 2001).
36. J.-A. Sepulchre and R. Mackay, Nonlinearity 10, 679 (1997).
37. O. E. Rössler, Phys. Lett. 57A, 397 (1976).
38. M. Hénon and C. Heiles, Astron. J. 69, 73 (1964).
39. V. Szebehely, Theory of Orbits (Academic Press, New York, 1967).
40. Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 55, 365 (1976).
41. G. I. Sivashinsky, Acta Astron. 4, 1177 (1977).
42. B. Nicolaenko, B. Scheurer, and R. Temam, Physica D 16, 155 (1985).