Newton's method and a class of meromorphic functions without wandering domains

DOI10.1017/S0143385700007343zbMath0781.58011MaRDI QIDQ3140460

Walter Bergweiler

Publication date: 13 February 1994

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

iterationdynamicsNewton's methodJulia setentire functionsFatou setmeromorphic functionsBaker domainwandering domains

Mathematics Subject Classification ID

Topological dynamics (37B99) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Meromorphic functions of one complex variable (general theory) (30D30) Special classes of entire functions of one complex variable and growth estimates (30D15)

Related Items (17)

A class of Newton maps with Julia sets of Lebesgue measure zero ⋮ Dynamics of Newton maps ⋮ Iteration of meromorphic functions ⋮ Note on wandering domains in the dynamics of solutions of certain difference equations ⋮ Dynamics of a family of transcendental meromorphic functions having rational Schwarzian derivative ⋮ On the dynamics of composite entire functions ⋮ Moduli space of cubic Newton maps ⋮ On entire function \(e^{p(z)}\int_0^z \beta (t)e^{-p(t)}dt\) with applications to Tumura-Clunie equations and complex dynamics ⋮ Dynamics of transcendental meromorphic functions (( )/( )) having rational Schwarzian derivatives ⋮ Some Connections of Complex Dynamics ⋮ Non-linear differential equations with transcendental meromorphic solutions ⋮ Some dynamical properties of transcendental meromorphic functions ⋮ Iteration of certain meromorphic functions with unbounded singular values ⋮ Explicit representation of structurally finite entire functions ⋮ Fatou components and singularities of meromorphic functions ⋮ On the simple connectivity of Fatou components ⋮ Wandering domains in the dynamics of certain meromorphic functions

Cites Work

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• Wandering Domains in the Iteration of Entire Functions
• Complex analytic dynamics on the Riemann sphere
• Iterates of Meromorphic Functions II: Examples of Wandering Domains
• On sullivan's classification of periodic stable domains
• Examples of Entire Functions with Pathological Dynamics
• The dynamics of rational transforms: the topological picture
• Iteration and the Zeros of the Second Derivative of a Meromorphic Function
• A class of meromorphic functions with no wandering domains

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