Symplectic maps for approximating polynomial Hamiltonian systems

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

Volumn 65, Issue 5, 2002, Pages

  Blanes, Sergio ^a  

^a University of Bath   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; COMPUTER SIMULATION; FUNCTIONS; POLYNOMIALS; SYNCHROTRON RADIATION;

ACCELERATOR PHYSICS; ITERATION ALGORITHMS; MOMENTA; POLYNOMIAL HAMILTONIAN SYSTEMS;

HAMILTONIANS;

EID: 37649027830     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.056703     Document Type: Article

References (32)

1. A. J. Dragt, in Physics of High Energy Particle Accelerators, edited by R. A. Carrigan, F. R. Huson, M. Month, AIP Conf. Proc. 87 (AIP, New York, 1982), 147-313.
2. A. J. Dragt, Lie Methods for Nonlinear Dynamics with Applications to Accelerator Physics (University of Maryland, Maryland, 2001).
3. A. J. Dragt, Phys. Rev. Lett. 75, 1946 (1995).
4. A. J. Dragt and D. T. Abell, in Integration Algorithms and Classical Mechanics, edited by J. E. Marsden, G. W. Patrick, and W. F. Shadwick, Fields Institute Communications Vol. 10 (American Mathematical Society, Providence, RI, 1996).
5. I. Gjaja, Part. Accel. 43, 133 (1994).
6. G. Rangarajan, A. J. Dragt, and F. Neri, Part. Accel. 28, 119 (1990).
7. J. Shi and Y. T. Yan, Phys. Rev. E 48, 3943 (1993).
8. P. J. Channell and C. Scovel, Nonlinearity 3, 231 (1990).
9. Y. Yan, P. Channell, and M. Syphers, SSCL Report No. 157, 1992 (unpublished).
10. J. S. Berg, R. L. Warnock, R. D. Ruth, and E. Forest, Phys. Rev. E 49, 722 (1994).
11. R. L. Warnock and J. A. Ellison, Appl. Numer. Math. 29, 89 (1999).
12. B. Erdélyi and M. Berz, Phys. Rev. Lett. 87, 114302 (2001).
13. G. Rangarajan and M. Sachidanand, J. Phys. A 33, 131 (2000).
14. J. Irwin, in Accelerator Physics at the Superconducting Super Collider, edited by Y. Yan, J. Naples, and M. Syphers, AIP Conf. Proc. 326 (AIP, New York, 1995). Originally written in 1989 as report SSC-228.
15. G. Rangarajan, J. Math. Phys. 37, 4514 (1996).
16. D. T. Abell, Ph.D. thesis, University of Maryland, 1995.
17. D. T. Abell, E. McIntosh, and S. Schmidt (unpublished).
18. A. J. Dragt and J. M. Finn, J. Math. Phys. 17, 2215 (1976).
19. L. Michelotti (unpublished).
20. J. Shi, Phys. Rev. E 50, 532 (1994).
21. R. D. Ruth, IEEE Trans. Nucl. Sci. NS-30, 2669 (1983).
22. E. Forest and R. D. Ruth, Physica D 43, 105 (1990).
23. M. Suzuki, Phys. Lett. A 146, 319 (1990).
24. H. Yoshida, Phys. Lett. A 150, 262 (1990).
25. J. M. Sanz-Serna and M. P. Calvo, Numerical Hamiltonian Problems (Chapman & Hall, London, 1994).
26. S. Blanes, F. Casas, and J. Ros, SIAM J. Sci. Comput. (USA) 21, 711 (1999).
27. S. Blanes, Appl. Numer. Math. 37, 289 (2001).
28. S. Blanes and P. C. Moan, J. Comput. Appl. Math. 142, 313 (2002).
29. P.-V. Koseleff, Formal Calculus for Lie Methods in Hamiltonian Mechanics, translation Ph.D. thesis, École Polytechnique, 1993, available as Lawrence Berkeley Laboratory Report No. LBID-2030, UC-405, 1994 (unpublished).
30. K. Feng and D. L. Wang, J. Comput. Math. 16, 97 (1998).
31. A. J. Dragt (private communication).
32. G. Rangarajan, J. Phys. A 31, 3649 (1998).