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Hyperbolic components of polynomials with a fixed critical point of maximal order. (English) Zbl 1151.37044
The author proves Milnor’s conjectures for complex one-dimensional slices of cubic polynomials with \(0\) is the critical fixed point and generates these results in higher degree. Furthermore, the author describes some important properties of the hyperbolic components and of the Mandelbrot copies sitting in the connected locus.

37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F15 Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
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