The dynamics of symmetric bimodal maps

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 7, Issue 12, 1997, Pages 2735-2744

  Lofaro, Thomas ^a  

^a WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031521592     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127497001849     Document Type: Article

References (19)

1. Chavoya-Aceves, O., Angulo-Brown, F. & Pina, E. [1985] "Symbolic dynamics of the cubic maps," Physica 14D, 374-386.
2. Collet, P. & Eckmann, J. P. [1980] Iterated Maps of the Interval as Dynamical Systems (Birkhauser, Boston).
3. Devaney, R. [1989] An Introduction to Chaotic Dynamical Systems, 2nd ed. (Addison-Wesley, Redwood City).
4. Fournier-Prunaret, D. [1982] "Structure de bifurcations d'un endomorphisme defini ar un polynôme du troisième degré," Compte Rendus Acad. Sc. Paris 294I, 455-458.
5. Fournier-Prunaret, D. [1987] "Structure de bifurcations d'un endomorphisme du cercle," Annales Telécommunications 42, 247-257.
6. Fournier-Prunaret, D. [1989] "Structure de bifurcations d'un endomorphisme du cercle en lui-même dans un plan de paramétres," in Proc. European Conf. Iteration Theory (ECIT 87) Caldes de Malavella (Spain) (World Scientific, Singapore), pp. 205-224.
7. Fournier-Prunaret, D. [1991] "Bifurcation structure of an endomorphism of the circle onto itself in a parameter plane," in Proc. European Conf. Iteration Theory (ECIT 89) Batschuns (Austria) (World Scientific, Singapore), pp. 117-126.
8. Gumowski, I. & Mira, C. [1980] "Dynamique chaotique, transformations ponctuelles, transition ordre- disordre," Cepadues Editions, Toulouse, 401-418.
9. Leipnik, R. B. & Newton, T. A. [1981] "Double strange attractors in rigid body motion with linear feedback control," Phys. Lett. 86A, 63-67.
10. Llibre, J. & Mumbru, P. [1989] "Renormalisation and periodic structure for bimodal maps," in Proc. European Conf. Iteration Theory (ECIT 87), Caldes de Malavella (Spain) (World Scientific, Singapore), pp. 253-262.
11. Llibre, J. & Mumbru, P. [1991] "Extending the *-product operator," in Proc. European Conf. Iteration Theory (ECIT 89), Batschuns (Austria) (World Scientific, Singapore), pp. 199-214.
12. LoFaro, T. [1997] "A model of the dynamics of the Newton-Leipnik attractor," Int. J. Bifurcation and Chaos 7(12), 2723-2733.
13. Mackay, R. S. & Tresser, C. [1987] "Some flesh on the skeleton: The bifurcation structure of bimodal maps," Physica 27D, 412-422.
14. Milnor, J. & Thurston, R. [1988] "On iterated maps of the interval," in Lecture notes in Mathematics, 1342, Dynamical Systems, ed. Alexander, J. C. (Springer- Verlag, New York), pp. 465-563.
15. Milnor, J. [1992] "Remarks on iterated cubic maps," Experimental Math. 1, 5-24.
16. Myrberg, P. J. [1963] "Iteration der reellen polynome zweiten grades n," Ann. Acad. Sci. Fenn. A336, 1-10.
17. Newton, T. A., Martin, D. & Leipnik, R. B. [1988] "A double strange attractor," in Dynamical Systems Approaches to Nonlinear Problems in Systems and Circuits, eds. Salam F. A. & Levi, M. L. (SIAM, Philadelphia), pp. 117-127.
18. Ringland. J. & Schell, M. [1991] "Genealogy and bifurcation skeleton for cycles of the iterated two-extremum map of the interval," SIAM J. Math. Anal. 22, 1354-1371.
19. Ringland, J. & Tresser, C. [1995] "A genalogy for finite kneading sequences of bimodal maps of the interval," Trans. AMS 347, 4599-4624.