The Fermi-Pasta-Ulam problem: Periodic orbits, normal forms and resonance overlap criteria

Physica D: Nonlinear Phenomena

Volumn 237, Issue 7, 2008, Pages 908-917

  Flach, S ^a   Ponno, A ^b  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^b UNIVERSITY OF PADOVA   (Italy)

Author keywords

Acoustic resonance; FPU problem; Periodic solutions

Indexed keywords

ACOUSTICS; PROBLEM SOLVING; RESONANCE;

FREQUENCY NORMAL MODES; PERIODIC ORBITS; PERIODIC SOLUTIONS; THRESHOLD VALUES;

FERMI LEVEL;

EID: 42249102774     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2007.11.017     Document Type: Article

References (33)

1. Fermi E., Pasta J., and Ulam S. Enrico Fermi-Note e Memorie (collected papers) vol. II (USA 1939-1954) (1965), Accademia Nazionale dei Lincei Roma (Italy), The University of Chicago Press, Chicago, USA p. 978
2. Ford J. Phys. Rep. 213 (1992) 271-310
3. Galgani L., and Scotti A. Phys. Rev. Lett. 28 (1972) 1173-1176
4. Ford J. J. Math. Phys. 2 (1961) 387-393
5. Izrailev F.M., and Chirikov B.V. Sov. Phys. Dokl. 11 (1966) 30-32
6. Shepelyansky D.L. Nonlinearity 10 (1997) 1331-1338
7. Flach S., Ivanchenko M.V., and Kanakov O.I. Phys. Rev. Lett. 95 (2005) 064102/1-4
8. Flach S., Ivanchenko M.V., and Kanakov O.I. Phys. Rev. E 73 (2006) 036618/1-14
9. Ivanchenko M.V., Kanakov O.I., Mishagin K.G., and Flach S. Phys. Rev. Lett. 97 (2006) 025505/1-4
10. Kanakov O.I., Flach S., Ivanchenko M.V., and Mishagin K.G. Phys. Lett. A 365 (2007) 416-420
11. Penati T., and Flach S. Chaos 17 (2007) 023102/1-16
12. Flach S., Kanakov O.I., Mishagin K.G., and Ivanchenko M.V. Internat J. Modern Phys. B 21 (2007) 3925-3931
13. Ponno A. Europhys. Lett. 64 (2003) 606-612
14. Ponno A. In: Collet P., et al. (Ed). Proceedings of the Cargése Summers School 2003 on Chaotic Dynamics and Transport in Classical and Quantum Systems (2005), Kluwer Achademic Publishers, Netherlands 431
15. Ponno A., and Bambusi D. In: Gaeta G., et al. (Ed). Proceedings of the International Conference on Symmetry and Perturbation Theory 2004 (2005), World Scientific Publishing, Singapore 263
16. Ponno A., and Bambusi D. Chaos 15 (2005) 015107
17. Bambusi D., and Ponno A. Comm. Math. Phys. 264 (2006) 539-561
18. D. Bambusi, A. Ponno, Review articles on Fermi-Pasta-Ulam Experiment grown out of the meeting, FPU fifty years later held in Rome (Italy) on May, 7th 2004 (to appear on a Springer Book edited by G. Gallavotti); available on the web site: http://ipparco.roma1.infn.it/index.html
19. Zabusky N.J., and Kruskal M.D. Phys. Rev. Lett. 15 (1965) 240-243
20. Berchialla L., Giorgilli A., and Paleari S. Phys. Lett. A 321 (2004) 167-172
21. Fucito F., et al. J. Physique 43 (1982) 707-713
22. Ford J., and Waters J. J. Math. Phys. 4 (1963) 1293-1306
23. A. Lyapunov, Problème général de la stabilité du mouvement, published by the Mathematical Society of Kharkov, 1892 (Russian). Available in Éditions Jacques Gabay, Paris (France) 1988 (French), reprint of the French translation from Russian appeared on the Annales de la Faculté des Sciences de Toulouse 2ème série, tome IX, 1907
24. De Luca J., Lichtenberg A., and Lieberman M.A. Chaos 5 (1995) 283-297
25. Berchialla L., Galgani L., and Giorgilli A. DCDS-A 11 (2004) 855-866
26. J.A. Biello, P.R. Kramer, Y.V. Lvov, Stages of energy transfer in the FPU model, DCDS Supplements, 2003, Special number devoted to the Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, Wilmington, NC, USA, May 24-27, 2002, p. 113
27. G. Benettin, R. Livi, A. Ponno, Work in progress
28. Giorgilli A., Paleari S., and Penati T. DCDS-B 5 (2005) 991-1004
29. Casetti L., Cerruti-Sola M., Pettini M., and Cohen E.G.D. Phys. Rev. E 55 (1997) 6566-6574
30. B.V. Chirikov, Internal Report n. 267 of the Nuclear Institute of the Siberian Section of the USSR Academy of Sciences, Novosibirsk, 1969; CERN Translation n. 70-41, Geneva 1971
31. Nayfeh A.H. Introduction to Perturbation Techniques (1993), Wiley, New York
32. Benettin G. Chaos 15 (2005) 015108
33. A. Lichtenberg, Private communication