Some Explicit Formulas for the Iteration of Rational Functions
نویسنده
چکیده
Let f be a rational function, which has k n-cycles under iteration. By using the symmetry of the underlying equation of degree k ·n, it is reduced to equations of degree k and n. This is explained in terms of Galois theory. The 3and 4-cycles of fc(z) = z2 + c are obtained explicitly. This yields the corresponding multiplier, which maps hyperbolic components of the Mandelbrot set conformally onto the unit disk.
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