Remark on the rational functions having the same Julia set

Details Remark on the rational functions having the same Julia set Remark on the rational functions having the same Julia set

1999-12-06

arxiv.org/abs/math/9912044v1

Mathematics

Complex Variables

17 pages

Scientific paper

Let f and g two rational functions having the same Julia set J_f. Lets
suppose that f has a rational indifferent periodic point and that the critical
set of f is disjoint of J_f. Then or J_f has to be equal to P^1, a circle, an
arc of a circle for some cordinate or f and g has to verify an equation of the
type: $$f^{m_1}\circ g\circ f^{m_2}\circ\cdotc\circ f^{m_n}\circ g=f^m.$$

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