Singularity confinement and chaos in discrete systems

Physical Review Letters

Volumn 81, Issue 2, 1998, Pages 325-328

  Hietarinta, Jarmo ^a   Viallet, Claude ^b  

^a UNIVERSITY OF TURKU   (Finland)

^b CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; CALCULATIONS; CHAOS THEORY; CONTROL SYSTEM ANALYSIS; ITERATIVE METHODS; POLYNOMIALS;

ALGEBRAIC ENTROPY; INTEGRABILITY; PAINLEVE TEST; SINGULARITY CONFINEMENT TEST;

DISCRETE TIME CONTROL SYSTEMS;

EID: 0032514086     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.81.325     Document Type: Article

References (17)

1. M. Henon, Q. J. Appl. Math. 27, 291–312 (1969);
2. G. Iooss, R. H. G. Helleman, and R. Stora (North-Holland, Amsterdam, 1983), pp. 53–170.
3. A. Nagai and J. Satsuma, Phys. Lett. A 209, 305–312 (1995).
4. S. V. Kovalevska, Acta Math. 12, 177–232 (1889).
5. P. Painlevé, C.R. Acad. Sci. (Paris) 130, 1112–1115 (1900).
6. A. Ramani, B. Grammaticos, and A. Bountis, Phys. Rep. 180, 159–245 (1989).
7. R. Conte, in The Painlevé Property, One Century Later, CRM Series in Mathematical Physics (Springer-Verlag, Berlin, 1998); solv-int/9710020.
8. B. Grammaticos, A. Ramani, and V. Papageorgiou, Phys. Rev. Lett. 67, 1825–1828 (1991).
9. A. Ramani, B. Grammaticos, and J. Hietarinta, Phys. Rev. Lett. 67, 1829–1831 (1991);
10. B. Grammaticos, F. W. Nijhoff, and A. Ramani, in The Painlevé Property, One Century Later Phys. Rev. Lett. 67, 1829–1831 (1991).
11. M. Bellon and C.-M. Viallet, chao-dyn/9805006, Report No. PAR-LPTHE 98-22.
12. G. Falqui and C.-M. Viallet, Commun. Math. Phys. 154, 111–125 (1993).
13. V. I. Arnold, Bol. Soc. Bras. Mat. 21, 1–10 (1990).
14. A. P. Veselov, Commun. Math. Phys. 145, 181–193 (1992).
15. S. Boukraa, J.-M. Maillard, and G. Rollet, Physica (Amsterdam) 209A, 162–222 (1994).
16. A. S. Fokas, B. Grammaticos, and A. Ramani, J. Math. Anal. Appl. 180, 342–360 (1993).
17. J.-P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57, 617–656 (1985).