On redefining a snap-back repeller

Chaos, Solitons and Fractals

Volumn 25, Issue 1, 2005, Pages 25-28

  Marotto, F R ^a  

^a FORDHAM UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; MATHEMATICAL MODELS; SET THEORY; THEOREM PROVING; TOPOLOGY; VECTORS;

CHAOTIC BEHAVIOR; HOMOCLINIC ORBIT; MULTIDIMENSIONAL MAPPING; SNAP-BACK REPELLER THEOREM;

CHAOS THEORY;

EID: 13544263211     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2004.10.003     Document Type: Article

References (18)

1. n J Math Anal Appl 63 1 1978 199 223
2. T.-Y. Li, and J. Yorke Period three implies chaos Am Math Mon 82 1975 985 992
3. F.R. Marotto Chaotic behavior in the Hénon mapping Commun Math Phys 68 1979 187 194
4. M. Scarowsky, and A. Boyarsky On n-dimensional piecewise-linear difference equations Nonlinear Anal Theor Meth Appl 4 4 1980 715 731
5. H.-O. Walther Homoclinic solution and chaos in x′(t) = f(x(t-1)) Nonlinear Anal Theor Meth Appl 5 3 1981 775 778
6. T. Rogers Remarks on multiparameter mappings: controlled-parameter and threshold maps Math Biosci 63 1983 57 69
7. H.C. Morris, E.E. Ryan, and R.K. Dodd Snap-back repellers and chaos in a discrete population model with delayed recruitment Nonlinear Anal Theor Meth Appl 7 6 1983 571 621
8. T. Rogers, and J.R. Pounder The evolution of crisis: bifurcation and demise of a snap-back repeller Physica D 13 1984 408 412
9. A. Dohtani Occurrence of chaos in higher-dimensional discrete-time systems SIAM J Appl Math 52 6 1992 1707 1721
10. L. Gardini, R. Abraham, R. Record, and D. Fournier-Prunaret A double logistic map Int J Bifurcat Chaos 4 1 1994 145 176
11. R. Lupini, S. Lenci, and L. Gardini Bifurcations and multistability in a class of two-dimensional endomorphisms Nonlinear Anal Theor Meth Appl 28 1 1997 61 85
12. R. Abraham, L. Gardini, and C. Mira Chaos in discrete dynamical systems: a visual introduction in 2 dimensions 1997 Springer-Verlag NY
13. L. Chen, and K. Aihara Chaos and asymptotical stability in a discrete-time neural network Physica D 104 1997 286 325
14. 2 Nonlinear Anal Theor Meth Appl 31 3/4 1998 455 458
15. S. Hassan Nonlinear difference equations: theory with application to social science models 2003 Kluwer Dordrecht, The Netherlands
16. C. Li, and G. Chen An improved version of the Marotto theorem Chaos, Solitons & Fractals 18 2003 69 77 Erratum: 20 (2004), p. 655
17. M. Hirsch, and S. Smale Differential equations, dynamical systems, and linear algebra 1974 Academic Press NY p. 278-281
18. S. Smale Differentiable dynamical systems Bull Am Math Soc 73 1967 747 817