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Zbl 1153.37329
Iglesias, J.; Portela, A.; Rovella, A.
Structurally stable perturbations of polynomials in the Riemann sphere. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 6, 1209-1220 (2008). ISSN 0294-1449

Summary: The perturbations of complex polynomials of one variable are considered in a wider class than the holomorphic one. It is proved that under certain conditions on a polynomial $p$ of the plane, the $C^r$ conjugacy class of a map $f$ in a $C^{1}$ neighborhood of $p$ depends only on the geometric structure of the critical set of $f$. This provides the first class of examples of structurally stable maps with critical points and nontrivial nonwandering set in dimension greater than one.

MSC 2000:: *37C20 Generic properties, structural stability
37C75 Stability theory
58K05 Critical points of functions and mappings

Keywords: structural stability; criticat set; complex polynomials

Cited in: Zbl 1251.37028 Zbl 1179.37029

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