Diophantine non-integrability of a third-order recurrence with the Laurent property

Journal of Physics A: Mathematical and General

Volumn 39, Issue 12, 2006, Pages

  Hone, A N W ^a  

^a UNIVERSITY OF KENT   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33644900487     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/12/L01     Document Type: Article

References (35)

1. Abarenkova N, Anglès d'Auriac J-C, Boukraa S, Hassani S and Maillard J-M 2000 J. Phys. A: Math. Gen. 33 1465
2. Ablowitz M J, Halburd R and Herbst B 2000 Nonlinearity 13 889
3. Baragar A 1994 J. Number Theory 49 27
4. Bobenko A I and Seiler R (ed) 1999 Discrete Integrable Geometry and Physics (Oxford: Oxford University Press)
5. Bobenko A I, Suris Y B and Mercat C 2005 J. Reine Angew. Math. 583 117
6. Button J O 1998 Bull. Lond. Math. Soc. 58 9
7. Conte R (ed) 1999 The Painlevé Property-One Century Later (CRM Series in Mathematical Physics) (Berlin: Springer)
8. Everest G, Miller V and Stephens N 2003 Proc. Am. Math. Soc. 132 955
9. Everest G, van der Poorten A, Shparlinski I and Ward T 2003 Recurrence Sequences (AMS Mathematical Surveys and Monographs vol 104) (Providence, RI: American Mathematical Society)
10. Fomin S and Zelevinsky A 2002 Adv. Appl. Math. 28 119
11. Gale D 1991 Math. Intelligencer 13 40
12. Grammaticos B, Ramani A and Papageorgiou V 1991 Phys. Rev. Lett. 67 1825
13. Halburd R G 2005 J. Phys. A: Math. Gen. 38 L1
14. Hietarinta J and Viallet C 1998 Phys. Rev. Lett. 81 325
15. Hone A N W 2005 Bull. Lond. Math. Soc. 37 161
16. Hone A N W 2005 Sigma function solution of the initial value problem for Somos-5 sequences Preprint math.NT/0501554 (Trans. Am. Math. Soc. at press)
17. Itsara A, Musiker G, Propp J and Viana R 2003 Combinatorial interpretations for the Markov numbers Preprint (web.mit.edu/∼ruilov/www/ markov.pdf)
18. Krichever I, Lipan O, Wiegmann P and Zabrodin A 1997 Commun. Math. Phys. 188 267
19. Markoff A A 1879 Math. Ann. 15 381
20. Mordell L J 1953 J. Lond. Math. Soc. 28 500
21. Noumi M 2004 Painlevé Equations Through Symmetry (AMS Translations of Mathematical Monographs vol 223) (Providence, RI: American Mathematical Society)
22. Okamoto K 1986 Math. Ann. 275 221
23. Perrine S 2002 La théorie de Markoff et ses développements (Chantilly: Tessier & Ashpool)
24. van der Poorten A 2005 J. Integer Sequences 8 article 05.2.5
25. Propp J 2001 Discrete Math. Theor. Comput. Sci. Proc. AA (DM-CCG) 43
26. Propp J 2005 The combinatorics of frieze patterns and Markoff numbers Preprint math.CO/0511633
27. Quispel G R W, Roberts J A G and Thompson C J 1989 Physica D 34 183
28. Ramani A, Grammaticos B and Satsuma J 1995 J. Phys. A: Math. Gen. 28 4655
29. Roberts J A G and Vivaldi F 2003 Phys. Rev. Lett. 90 034102
30. Sakai H 2001 Commun. Math. Phys. 220 165
31. Speyer D E 2004 Perfect matchings and the octahedron recurrence Preprint math.CO/0402452
32. Swart C S 2003 Elliptic curves and related sequences PhD Thesis University of London
33. Veselov A P 1991 Russ. Math. Surv. 46 1
34. Veselov A P 1992 Commun. Math. Phys. 145 181
35. Zabrodin A 1997 Teor. Mat. Fiz. 113 1347 (Preprint solv-int/9704001)