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A lot is known about the forward iterates of an analytic function which is bounded by 1 in modulus on the unit disk D. The Denjoy-Wolff Theorem describes their convergence properties and several authors, from the 1880's to the 1980's, have provided conjugations which yield very precise descriptions of the dynamics. Backward-iteration sequences are of a different nature because a point could have infinitely many preimages as well as none. However, if we insist in choosing preimages that are at a...

Baker domains for Newton’s method

Walter Bergweiler, David Drasin, James 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 $f (z) \sim exp (- z^{n}), n \in ℕ$ , 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 direction...

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Analytic First Integrals of Ordinary Differential Equations

Analytic mappings between two ultrahyperelliptic surfaces.

Analytic mappings between two ultrahyperelliptic surfaces. (Short Communication).

Analytic solutions of Böttcher's functional equation in the unit disk.

Applications de la théorie de Nevanlinna p-adique.

Area and Hausdorff dimension of the set of accessible points of the Julia sets of λe^z and λ sin(z)

Asymptotic behaviors of complex analytic dynamical systems.

Asymptotische Selbstentwicklungen von holomorphen Funktionen.

Attracting dynamics of exponential maps.

Attractive Cycles in the Iteration of Meromorphic Functions.

Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk.

Baker domains for Newton’s method

Behavior of the trinomial arcs $B (n, k, r)$ when $0 < α < 1$ .

Boundaries of unbounded Fatou components of entire functions.

Canonical conjugations at fixed points other than the Denjoy-Wolff point.

Cauchy's functional equation in restricted complex domains.

Characteristic functional equations of polynomials and the Morera-Carleman theorem.

Complex a priori bounds revisited

Complex Analytic and Formal Solutions of Real Analytic Equations in Cn.

Components of degree two hyperbolic rational maps.

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