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Using dynamical methods we give a new proof of the theorem saying that if A, B, X are rational functions of complex variable z of degree at least two such that $$A\circ… Click to show full abstract
Using dynamical methods we give a new proof of the theorem saying that if A, B, X are rational functions of complex variable z of degree at least two such that $$A\circ X=X\circ B$$A∘X=X∘B and $${\mathbb C}(B,X)={\mathbb C}(z)$$C(B,X)=C(z), then the Galois closure of the field extension $${\mathbb C}(z)/{\mathbb C}(X)$$C(z)/C(X) has genus zero or one.
Keywords:
rational functions;
functions dynamical;
semiconjugate rational;
dynamical approach
Journal Title: Arnold Mathematical Journal
Year Published: 2017
Link to full text (if available)
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Journal Title: Arnold Mathematical Journal
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!