Some Explicit Formulas for the Iteration of Rational Functions

  • Wolf Jung
  • Published 1997

Abstract

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… (More)

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