Dynamics of some rational discrete dynamical systems via invariants

International Journal of Bifurcation and Chaos

Volumn 16, Issue 3, 2006, Pages 631-645

  Cima, Anna ^a   Gasull, Armengol ^a   Mañosa, Víctor ^b  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Discrete dynamical system; First integral; M bius transformation; Nonautonomous invariant; Riccati differential equation; Rotation number

Indexed keywords

MATHEMATICAL TRANSFORMATIONS; NUMBER THEORY; RICCATI EQUATIONS;

DISCRETE DYNAMICAL SYSTEM; MÖBIUS TRANSFORMATION; NONAUTONOMOUS INVARIANT; RICCATI DIFFERENTIAL EQUATION; ROTATION NUMBER;

NONLINEAR SYSTEMS;

EID: 33744759647     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127406015027     Document Type: Article

References (11)

1. Bastien, G. & Rogalski, M. [2004] "Global behavior of the solutions of Lynes difference equation," J. Diff. Eqs. Appl. 10, 977-1003.
2. Beukers, F. & Cushman, R. [1998] "Zeeman's monotonicity conjecture," J. Diff. Eqs. 143, 191-200.
3. Cima, A., Gasull, A. & Mañosas, F. [2004] "On periodic rational difference equations of order k," J. Diff. Eqs. Appl. 10, 549-559.
4. Devaney, R. L. [2003] An Introduction to Chaotic Dynamical Systems (Westview Press, Boulder, CO).
5. Gardini, L., Bischi, G. I. & Mira, C. [2001] "Invariant curves and focal points in a Lyness iterative process," Int. J. Bifurcation and Chaos 13, 1841-1852.
6. Gasull, A. & Mañosa, V. [2002] "A Darboux-type theory of integrability for discrete dynamical systems," J. Diff. Eqs. Appl. 8, 1171-1191.
7. Goriely, A. [2001] Integrability and Nonintegrability of Dynamical Systems, Advanced Series in Nonlinear Dynamics, Vol. 19 (World Scientific, Singapore).
8. Hille, E. [1976] Ordinary Differential Equations in the Complex Domain (Dover Publications, NY).
9. Kulenović, M. R. S. [2000] "Invariants and related Liapunov functions for difference equations," Appl. Math. Lett. 13, 1-8.
10. j 0 ≤ t ≤ 1 for which x(0) = x(1)," Inv. Math. 59, 67-76.
11. Zeeman, E. C. [1996] "Geometric unfolding of a difference equation," preprint, Hertford College, Oxford.