Real continuation from the complex quadratic family: Fixed-point bifurcation sets

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 10, Issue 2, 2000, Pages 391-414

  Peckham, Bruce B ^a   Montaldi, James ^b  

^a UNIVERSITY OF MINNESOTA DULUTH   (United States)

^b UNIVERSITÉ CÔTE D'AZUR   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CARDIOIDEA;

EID: 0034134827     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127400000256     Document Type: Article

References (11)

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2. Bogdanov, R. I. [1976] "Versal deformation of a singularity of a vector field in the plane in the case of zero eigenvalues," Trudy Seminara Imeni I. G. Petrovskogo, Vol. 2, pp. 23-36; English translation [1981] Selecta Math. Sovietica 1(4), 389-421.
3. Bogdanov, R. I. [1976] "Versal deformation of a singularity of a vector field in the plane in the case of zero eigenvalues," Trudy Seminara Imeni I. G. Petrovskogo, Vol. 2, pp. 23-36; English translation [1981] Selecta Math. Sovietica 1(4), 389-421.
4. Carleson, L. & Gamelin, T. W. [1993] Complex Dynamics (Springer-Verlag, NY).
5. Drexler, J. [1966] "A nonanalytic perturbation of the complex quadratic family of maps," Master's Project University of Minnesota, Duluth, Technical Report 96-5.
6. Golubitsky, M. & Schaeffer, D. [1985] Singularities and Groups in Bifurcation Theory, Vol. I, Applied Mathematical Sciences 51 (Springer Verlag, NY).
7. Nien, C.-H. [1998] "The dynamics of planar quadratic maps with nonempty bounded critical set," Int. J. Bifurcation and Chaos 8(1), 95-105.
8. Nien, C.-H. [1997] "The investigation of a saddlenode bifurcation with a zero eigenvalue -includes examle of nonanalyticity," PhD thesis, University of Minnesota.
9. Peckham, B. B. [1988-1998] To Be Continued ..., a continuation software package for discrete dynamical systems (continually under development).
10. Peckham, B. B. [1998] "Real perturbation of complex analytic families: Points to regions," Int. J. Bifurcation and Chaos 8(1), 73-93.
11. Takens, F. [1974] "Forced oscillations and bifurcations," Applications of Global Analysis, Communications of the Mathematical Institute Rijksuniversiteit Utrecht, Vol. 3, pp. 1-59.