Structurally stable perturbations of polynomials in the Riemann sphere

Iglesias, J.; Portela, A.; Rovella, A.

doi:10.1016/j.anihpc.2008.02.001

Iglesias, J. ; Portela, A. ; Rovella, A.

Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 6, pp. 1209-1220

EuDML MR Zbl

DOI : 10.1016/j.anihpc.2008.02.001

@article{AIHPC_2008__25_6_1209_0,
     author = {Iglesias, J. and Portela, A. and Rovella, A.},
     title = {Structurally stable perturbations of polynomials in the {Riemann} sphere},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1209--1220},
     year = {2008},
     publisher = {Elsevier},
     volume = {25},
     number = {6},
     doi = {10.1016/j.anihpc.2008.02.001},
     mrnumber = {2466327},
     zbl = {1153.37329},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2008.02.001/}
}

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Iglesias, J.; Portela, A.; Rovella, A. Structurally stable perturbations of polynomials in the Riemann sphere. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 6, pp. 1209-1220. doi: 10.1016/j.anihpc.2008.02.001

Bibliographie
Cité par

[1] Aoki N., Moriyasu K., Sumi N., $C^{1}$ maps having hyperbolic periodic points, Fund. Math. 169 (2001) 1-49. | Zbl | MR | EuDML

[2] Franks J., Necessary conditions for stability of diffeomorphisms, Trans. Amer. Math. Soc. 158 (1971) 301-308. | Zbl | MR

[3] Golubitsky M., Guillemin V., Stable Mappings and Their Singularities, Graduate Texts in Mathematics, vol. 14, Springer, New York, 1973. | Zbl | MR

[4] Hirsch M., Differential Topology, Springer-Verlag, New York, 1976. | Zbl | MR

[5] Iglesias J., Portela A., Real Perturbations of complex polynomials, Bull. Braz. Math. Soc. (N.S.) 38 (1) (2007) 129-155. | Zbl | MR

[6] Mañé R., A proof of the $C^{1}$ stability conjecture, Publ. Math. Inst. Hautes Études Sci. 66 (1987) 161-210, (in English). | Numdam | Zbl | MR | EuDML

[7] Mañé R., Sad P., Sullivan D., On the dynamics of rational maps, Ann. Sci. École Norm. Sup. (4) 16 (2) (1983) 193-217. | Numdam | Zbl | MR | EuDML

[8] Milnor J., Dynamics in One Complex Variable, Annals of Mathematics Studies, vol. 160, Princeton Univ. Press, 2006. | Zbl | MR

[9] Przytycki F., On Ω-stability and structural stability of endomorphisms satisfying Axiom A, Studia Math. 60 (1976) 61-77. | Zbl | MR | EuDML

[10] Robinson C., Structural stability of $C^{1}$ diffeomorphisms, J. Differential Equations 22 (1976) 28-73. | Zbl | MR

[11] Shub M., Endomorphisms of compact differentiable manifolds, Amer. J. Math. 91 (1969) 175-199. | Zbl | MR

[12] Steinmetz N., Rational Iteration, de Gruyter Studies in Mathematics, vol. 16, 1993. | Zbl | MR

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