Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi - Pasta - Ulam lattices by the generalized alignment index method

European Physical Journal: Special Topics

Volumn 165, Issue 1, 2008, Pages 5-14

  Skokos, C ^a   Bountis, T ^b   Antonopoulos, C ^b  

^a OBSERVATOIRE DE PARIS   (France)

^b UNIVERSITY OF PATRAS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 58049218995     PISSN: 19516355     EISSN: 19516401     Source Type: Journal    
DOI: 10.1140/epjst/e2008-00844-2     Document Type: Article

References (23)

1. B.V. Chirikov, Phys. Rep. 180, 179 (1979)
2. R.S. MacKay, J.D. Meiss, Hamiltonian Dynamical Systems (Adam Hilger, Bristol, 1987)
3. M.A. Lieberman, A.J. Lichtenberg, Regular and Chaotic Dynamics (Springer Verlag, 1992)
4. G. Contopoulos, Order and Chaos in Dynamical Astronomy (Springer, Berlin, 2002)
5. Nonlinear Problems in Future Particle Accelerators, edited by W. Scandale, G. Turchetti (World Scientific, Singapore, 1991); T. Bountis, Ch. Skokos, Nucl. Instrum. Meth. Res. A 561, 173 (2006)
6. S.C. Farantos, Z.-W. Qu, H. Zhu, R. Scinke, Int. J. Bifur. Chaos. 16, 1913 (2006)
7. C. Jung, H.S. Taylor, E.L. Sibert, J. Phys. Chem. A 110, 5317 (2006)
8. S. Flach, M.V. Ivanchenko, O.I. Kanakov, Phys. Rev. Lett. 95, 064102 (2005)
9. J. Ford, Phys. Rep. 213, 271 (1992); G.P. Berman, F.M. Izrailev, Chaos 15, 015104 (2005)
10. G. Benettin, L. Galgani, A. Giorgilli, J.-M. Strelcyn, Meccanica 15, 9 (1980)
11. G. Benettin, L. Galgani, A. Giorgilli, J.-M. Strelcyn, Meccanica 15, 21 (1980)
12. Ch. Skokos, T.C. Bountis, Ch. Antonopoulos, Physica D 231, 30 (2007)
13. Ch. Skokos, J. Phys. A 34, 10029 (2001); Ch. Skokos, Ch. Antonopoulos, T.C. Bountis, M.N. Vrahatis, Prog. Theor. Phys. Supp. 150, 439 (2003); Ch. Skokos, Ch. Antonopoulos, T.C. Bountis, M.N. Vrahatis, J. Phys. A 37, 6269 (2004)
14. F.F. Karney, Physica D 8, 360 (1983); J.D. Meiss, E. Ott, Phys. Rev. Lett. 55, 2741 (1985); V. Afraimovich, G.M. Zaslavsky, Lect. Notes Phys. 511, 59 (1998); Ch. Efthymiopoulos, G. Contopoulos, N. Voglis, R. Dvorak, J. Phys. A 30, 8167 (1997); R. Dvorak, G. Contopoulos, Ch. Efthymiopoulos, N. Voglis, Planet. Space Sci. 46, 1567 (1998)
15. M. Spivak, Comprehensive Introduction to Differential Geometry, Vol. 1 (Publ. or Per. Inc., 1999)
16. Ch. Antonopoulos, T. Bountis, Romai J. 2, 1 (2006); see also Ch. Antonopoulos, Ph.D. Thesis, Department of Mathematics, University of Patras, 2007
17. J.H. Hubbard, B.B. Hubbard, Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach, Chapter 5 (Prentice Hall, 1999)
18. N. Bourbaki, Éléments de mathématique, Livre II: Algèbre, Chapitre 3 (Hermann, 1958)
19. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, Chapter 2 (Cambridge University Press, 2003)
20. R.I. McLachlan, G.R.W. Quispel, J. Phys. A 39, 5251 (2006)
21. P.J. Prince, J.R. Dormand, J. Comp. Appl. Math. 7, 67 (1981)
22. E. Christodoulidi, T. Bountis, Romai J. 2, 37 (2006)
23. O. Merlo, L. Benet, Cel. Mech. Dyn. Astr. 97, 49 (2007)