An algorithm for the computation of preimages in noninvertible mappings

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 8, Issue 2, 1998, Pages 415-422

  Nien, Chia Hsing ^a   Wicklin, Frederick J ^b  

^a PROVIDENCE UNIVERSITY   (Taiwan)

^b SAS INSTITUTE INC   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032008390     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127498000279     Document Type: Article

References (12)

1. Allgower, E. L. & Georg, K. [1990] Numerical Continuation Methods, an Introduction (Springer-Verlag).
2. Arnold, V. I. [1981] Singularity Theory (London Mathematical Society).
3. Devaney, R. [1985] An Introduction to Chaotic Dynamical Systems (Benjamin Cummings, Menlo Park, CA).
4. Frouzakis, C. E., Adomaitis, R. A., Kevrekidis, I. G., Golden, M. P. & Ydstie, B. E. [1992] "The structure of basin boundaries in a simple adaptive control system," in Chaotic Dynamics: Theory and Practice, ed. Bountis, T. (Plenum Press), pp. 195-210.
5. Frouzakis, C. E., Gardini, L., Kevrekidis, I. G., Millerioux, G. & Mira, C. [1997] "On some properties of invariant sets of two-dimensional noninvertible maps," Int. J. Bifurcation and Chaos 7(6), 1167-1194.
6. Gilmore, R. [1981] Catastrophe Theory for Scientists and Engineers (Wiley).
7. Golubitsky, M. & Guillemin, V. [1973] Stable Mappings and Their Singularities (Springer-Verlag, New York).
8. Henle, M. [1979] A Combinatorial Introduction to Topology (Dover).
9. Mira, C., Carcassès, J.-P., Millérioux, G. & Gardini, L. [1995] "Plane foliations of two-dimensional noninvertible maps, Technical Report, Groupe d'Etudes des Systémes Non Linèaires et Applications, LESIA.
10. Mira, C. & Narayaninsamy, T. [1993] "On behaviors of two-dimensional endomorphisms: Role of the critical curves," Int. J. Bifurcation and Chaos 3(1), 187-194.
11. Whitney, H. [1955] "On singularities of mappings of Euclidean space I: Mappings of the plane into the plane," Annals of Mathematics 62, 374-410.
12. Wicklin, F. J. [1995] "Pisces: A platform for implicit surfaces and curves and the exploration of singularities," Technical Report GCG #89, The Geometry Center, University of Minnesota.