Global behavior of the solutions of Lyness' difference equation u n+2un = un+1 + a

Journal of Difference Equations and Applications

Volumn 10, Issue 11, 2004, Pages 977-1003

  Bastien, G ^a   Rogalski, M ^b  

^a INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

^b UNIVERSITÉ LILLE 1   (France)

Author keywords

Difference equations; Dynamical systems; Lyness sequence; Periods

Indexed keywords

EID: 4544284929     PISSN: 10236198     EISSN: None     Source Type: Journal    
DOI: 10.1080/10236190410001728104     Document Type: Article

References (16)

1. A. M. Amleh and G. Ladas, Convergence to periodic solutions, in Open Problems and Conjectures, Journal of Difference Equations and Applications 7 (2001), 621-631.
2. P. Appel and E. Lacour, Principes de la théorie des fonctions elliptiques, Gauthier-Villars, Paris, 1897.
3. E. Barbeau, B. Gelbord and S. Tanny, Periodicities of solutions of the generalized Lyness recursion, Journal of Difference Equations and Applications 1 (1995), 291-306.
4. +, a and b ≥ 0, Radovi Matematički 12 (2004), 135-152.
5. +, related to families of conics or cubics: generalization of Lyness' sequences", To appear in J. Math. Analysis and Appl.
6. J. C. Carrega, Théorie des corps. La règle et le compas, Hermann, Paris, 1981.
7. C. Darwen and W. T. Patula, Properties of a certain Lyness equation, Journal of Mathematical Analysis and Applications 218 (1998), 458-478.
8. n-1, Communications on Applied Nonlinear Analysis 1(3) (1994), 61-72.
9. D. Husemoller, Elliptic Curves, Springer-Verlag, New York, 1987.
10. V. L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993.
11. V. L. Kocic, G. Ladas and I. W. Rodrigues, On rational recursive sequences, Journal of Mathematical Analysis and Applications 173 (1993), 127-157.
12. R. C. Lyness, Notes 1581, 1847 and 2952, Mathematical Gazette 26 (1942), 62; 29 (1945) 231; and 45; 201 (1961).
13. R. C. Lyness, Notes 1581, 1847 and 2952, Mathematical Gazette 26 (1942), 62; 29 (1945) 231; and 45; 201 (1961).
14. R. C. Lyness, Notes 1581, 1847 and 2952, Mathematical Gazette 26 (1942), 62; 29 (1945) 231; and 45; 201 (1961).
15. G. Robin, Estimation de la fonction de Tchebychef Θ sur le k-ième nombre premier et grandes valeurs de la fonction to ω (n) nombre de diviseurs premiers de n, Acta Arithmetica XLII (1983), 367-389.
16. G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres Cours spécialisé no. 1, Collection Société Mathématique de France, Paris, 1995.