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Baker domains for Newton’s method

Walter BergweilerDavid DrasinJames K. Langley — 2007

Annales de l’institut Fourier

For an entire function f let N ( z ) = z - f ( z ) / f ( z ) be the Newton function associated to f . Each zero ξ of f is an attractive fixed point of N and is contained in an invariant component of the Fatou set of the meromorphic function N in which the iterates of N converge to ξ . If f has an asymptotic representation f ( z ) exp ( - z n ) , n , in a sector | arg z | < ε , then there exists an invariant component of the Fatou set where the iterates of N tend to infinity. Such a component is called an invariant Baker domain. A question in the opposite...

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