Invariant curves and focal points in a Lyness iterative process

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 13, Issue 7, 2003, Pages 1841-1852

  Gardini, L ^a   Bischi, G I ^a   Mira, C ^a  

^a NONE

Author keywords

Focal points; Lyness equations; Rational maps; Recurrences

Indexed keywords

FUNCTIONS; MAPS; MATHEMATICAL MODELS; THEOREM PROVING;

INVARIANT CURVES;

ITERATIVE METHODS;

EID: 0141730336     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127403007679     Document Type: Conference Paper

References (12)

1. Bischi, G. I. & Gardini, L. [1997] "Basin fractalization due to focal points in a class of triangular maps," Int. J. Bifurcation and Chaos 7, 1555-1557.
2. Bischi, G. I., Gardini, L. & Mira, C. [1999a] "Maps with denominator. Part 1: Some generic properties," Int. J. Bifurcation and Chaos 9, 119-153.
3. Bischi, G. I., Gardini, L. & Mira, C. [1999b] "New phenomena related to the presence of focal points in two-dimensional maps," Ann. Math. Silesianae (special issue Proc. ECIT98) 13, 81-90.
4. Bischi, G. I., Mira, C. & Gardini, L. [2000] "Unbounded sets of attraction," Int. J. Bifurcation and Chaos 10, 1437-1469.
5. Csornyei, M. & Laczkovich, M. [2001] "Some periodic and non-periodic recursions," Monatshefte für Mathematik 132, 215-236.
6. Kocic, V. I. & Ladas, G. [1993] Global Behaviour of Nonlinear Difference Equations of Higher Order with Applications (Kluwer Academic Publishers, the Netherlands).
7. Kocic, V. I., Ladas, G. & Rodrigues, I. W. [1993] "On rational recursive sequences," J. Math. Anal. Appl. 173, 127-157.
8. Lin, J. & Liu, Z. [1999] "Invariant curves of the generalized Lynass equations," Int. J. Bifurcation and Chaos 9, 1443-1450.
9. Lyness, R. C. [1942] "Note 1581," The Mathematical Gazette 26, p. 62.
10. Lyness, R. C. [1945] "Note 1847," The Mathematical Gazette 29, 231-233.
11. Lyness, R. C. [1961] "Note 2952," The Mathematical Gazette 45, 207-209.
12. 2) maps not defined in the whole plane," Grazer Math. Berichte (special issue Proc. ECIT96) 339, 261-278.