Plane maps with denominator. Part II: Noninvertible maps with simple focal points

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 13, Issue 8, 2003, Pages 2253-2277

  Bischi, Gian Italo ^a   Gardini, Laura ^a   Mira, Christian ^a  

^a NONE

Author keywords

Focal points; Noninvertible maps; Prefocal sets; Vanishing denominator

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTATIONAL GEOMETRY; ITERATIVE METHODS; SET THEORY;

FOCAL POINTS;

CHAOS THEORY;

EID: 0242666444     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021812740300793X     Document Type: Article

References (17)

1. Abraham, R., Gardini, L. & Mira, C. [1997] Chaos in Discrete Dynamical Systems (A Visual Introduction in Two Dimension) (Springer-Verlag).
2. Billings, L. & Curry, J. H. [1996] "On noninvertible maps of the plane: Eruptions," Chaos 6, 108-119.
3. Billings, L., Curry, J. H. & Phipps, E. [1997] "Lyapunov exponents, singularities, and a riddling bifurcation," Phys. Rev. Lett. 79, 1018-1021.
4. Bischi, G. I. & Gardini, L. [1997] "Basin fractalization due to focal points in a class of triangular maps," Int. J. Bifurcation and Chaos 7, 1555-1577.
5. Bischi, G. I. & Naimzada, A. [1997] "Global analysis of a nonlinear model with learning," Econ. Notes 26, 143-174.
6. Bischi, G. I. & Gardini, L. [1999] "Focal points and basin fractalization in some rational maps," in the Grazer Mathematische Berichte (Special Issue Proc. ECIT96), Nr. 339, pp. 61-84.
7. Bischi, G. I., Gardini, L. & Mira, C. [1999] "Maps with denominator. Part 1: Some generic properties," Int. J. Bifurcation and Chaos 9, 119-153.
8. Bischi, G. I., Gardini, L. & Mira, C. [2001a] "Maps with a vanishing denominator. A survey of some results," Nonlin. Anal. T.M.&A. (Special Issue Proc. WCNA2000) 47, 2171-2185.
9. Bischi, G. I., Kopel, M. & Naimzada, A. [2001b] "On a rent-seeking game described by a non-invertible iterated map with denominator," Nonlin. Anal. T.M.&A. (Special Issue Proc. WCNA2000) 47, 5309-5324.
10. Brock, W. A. & Hommes, C. H. [1997] "A rational route to randomness," Econometrica 65, 1059-1095.
11. Gardini, L., Bischi, G. I. & Fournier-Prunaret, D. [1999] "Basin boundaries and focal points in a map coming from Bairstow's methods," Chaos 9, 367-380.
12. Gumowski, I. & Mira, C. [1980] Dynamique Chaotique (Cepadues Editions, Toulouse).
13. Mira, C., Fournier-Prunaret, D., Gardini, L., Kawakami, H. & Cathala, J. C. [1994] "Basin bifurcations of two-dimensional noninvertible maps: Fractalization of basins," Int. J. Bifurcation and Chaos 4, 343-381.
14. Mira, C., Gardini, L., Barugola, A. & Cathala, J. C. [1996a] Chaotic Dynamics in Two-Dimensional Noninvertible Maps (World Scientific, Singapore).
15. Mira, C., Millerioux, G., Carcasses, J. P. & Gardini, L. [1996b] "Plane foliation of two-dimensional noninvertible maps," Int. J. Bifurcation and Chaos 6, 1439-1462.
16. 2) maps not defined in the whole plane," in the Grazer Mathematische Berichte (Special Issue Proc. ECIT96), Nr. 339, pp. 261-278.
17. Yee, H. C. & Sweby, P. K. [1994] "Global asymptotic behavior of iterative implicit schemes," Int. J. Bifurcation and Chaos 4, 1579-1611.