About two-dimensional piecewise continuous noninvertible maps

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 6, Issue 5, 1996, Pages 893-918

  Christian, Mira ^a  

^a INSA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030135552     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127496000503     Document Type: Article

References (34)

1. Afraimovich, V. S., Bukov, V. V. & Shilnikov, L. P. [1977] "Birth and structure of the Lorenz attractor," Dokl. Akad. Nauk SSSR 234(2), 336-339.
2. Barugola, A., Cathala, J. C. and Mira, C. [1986] "Annular chaotic areas," Nonlinear Analysis T.M. & A. 10(11), 1223-1236.
3. Barugola, A. & Cathala, J. C. [1992] "An extension of the notion of chaotic area in two-dimensional endomorphisms," European Conf. on Iteration Theory, Batschuns, Austria, Sept. 92.
4. Barugola, A., Cathala, J. C. & Mira, C. [1995] "Extension of the motion of chaotic area in second order endomorphisms," Int. J. Bifurcation and Chaos 5(3), 751-778.
5. Cathala, J. C. [1989] "On some properties of absorptive areas in 2nd order ndomorphisms," ECIT Batschuns, Sept. 1989 (World Scientific).
6. Cathala, J. C. [1990] "Multi-connected chaotic areas in second order endomorphisms," Int. J. Syst. Sci. 21(5), 863-887.
7. Fatou, P. [1919, 1920] "Memoire sur les équations fonctionnelles," Bull. Soc. Math. France 47, 161-271; 48, 33-94, 208-314.
8. Fatou, P. [1919, 1920] "Memoire sur les équations fonctionnelles," Bull. Soc. Math. France 47, 161-271; 48, 33-94, 208-314.
9. Feely, O. & Chua, L. O. [1992] "Nonlinear dynamics of a class of analogue-to-digital converters," Int. J. Bifurcation and Chaos 2(2), 325-340.
10. Feely, O. [1994]. "Nonlinear dynamics and chaos in Sigma-Delta modulation," J. of The Franklin Institute 331B(6), 903-936.
11. Gardini, L. [1991] "On the global bifurcation of two-dimensional endomorphisms by use of critical lines," Nonlinear Analysis T.M. & A. 18(4), 361-399.
12. Gardini, L. [1991a] "Global analysis and bifurcations in two-dimensional endomorphisms by use of critical lines," Proc. of ECIT, European Conf. on Iteration Theory, Batschuns, Austria, Sept. 91 (World Scientific, Singapore, 1992), pp. 112-125.
13. Gardini, L. [1992] "Homoclinic orbits of saddles in two-dimensional endomorphisms," Proc. of ECIT European Conference on Iteration Theory, Batschuns, Austria, Sept. 1992.
14. Gardini, L. [1993] "On a model of financial crisis. Critical lines as new tools of global analysis," Nonlinear Dynamics in Economics and Social Sciences, ed. Gori & Geronazzo (Springer-Verlag, 1993).
15. Gardini, L., Abraham, R., Fournier-Prunaret, D. & Record, R. J. [1994] "A double logistic map," Int. J. Bifurcation and Chaos 4(1), 145-176.
16. Gardini, L. [1994] "Homoclinic bifurcations in n-dimensional endomorphisms due to expanding periodic points," Nonlinear analysis T.M. & A. 23(8), 1039-1089.
17. Gumowski, I. & Mira, C. [1965] "Sur un algorithme de détermination du domaine de stabilité d'un point double d'une récurrence non linéaire du deuxième ordre à variables réelles," Comptes Rendus Acad. Sc. Paris, Série A 260, 6524-6527.
18. Gumowski, I. & Mira, C. [1977] "Solutions chaotiques bornées d'une récurrence ou transformation ponctuelle du second ordre à inverse non unique," Comptes Rendus Acad. Sc. Paris, Série A 285, 477-480.
19. Gumowski, I. & Mira, C. [1978] "Bifurcation déstabilisant une solution chaotique d'un endomorphisme du 2nd ordre," Comptes Rendus Acad. Sc. Paris, Série A 286, 427-431.
20. Gumowski, I. & Mira, C. [1980] Dynamique Chaotique, ed. Cépadues, Toulouse.
21. Gumowski, I. & Mira, C. [1980a] "Recurrences and discrete dynamic systems," Lecture Notes in Mathematics, Vol. 809 (Springer).
22. Julia, G. [1918] "Mémoire sur l'itération des fonctions rationnelles," J. Math. Pure Appl. 4(1), 47-245.
23. 2(t) = b," Bull. Faculty of Engineering, Tokushima University, 16, 29-46.
24. n," J. Math. Analysis Appl. 63, 199-223.
25. Mira, C. [1966] "Sur quelques propriétés de la frontière du domaine de stabilité d'un point double d'une récurrence du deuxième ordre à variables réelles et sur un cas de bifurcation de cette frontiére," Comptes Rendus Acad. Sc. Paris, Série A 262, 951-954.
26. Mira, C. [1980] "Complex dynamics in two-dimensional endomorphisms," Nonlinear Analysis, T.M. & A. 4(6), 1167-1187.
27. Mira, C. [1987] Chaotic Dynamics (World Scientific, Singapore).
28. Mira, C. & Roubellat, J. C. [1969] "Cas où le domaine de stabilité d'un ensemble limite attractif d'une récurrence du deuxième ordre n'est pas simplement connexe," Comptes Rendus Acad. Sc. Paris, Série A 268, 1657-1660.
29. Mira, C. & Narayaninsamy, T. [1993] "On two behaviors of two-dimensional endomorphisms: Role of the critical curves," Int. J. Bifurcation and Chaos 3(1), 187-194.
30. 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(2), 343-381.
31. Mira, C., Gardini, L., Barugola, A. & Cathala, J. C. [1996] Chaotic Dynamics in Two-Dimensional Noninvertible Maps, to appear in series on Nonlinear Science, (World Scientific).
32. Mira, C., Carcasses, J.-P., Millérioux, G. & Gardini, L. [1996] "Plane foliation of two-dimensional noninvertible maps," to appear in Int. J. Bifurcation and Chaos.
33. Mira, C. & Rauzy, C. [1995] "Fractal aggregation of basin islands in two-dimensional quadratic noninvertible maps," Int. J. Bifurcation and Chaos 5(4), 991-1019.
34. Sharkovskij, A. N. [1969] "Problem of the isomorphism of dynamical systems," Proc. of 5th Int. Conf. of Nonlinear Oscillations, Kiev, Vol. 2, pp. 541-544.