منابع مشابه
Boundaries of Escaping Fatou Components
Let f be a transcendental entire function and U be a Fatou component of f . We show that if U is an escaping wandering domain of f , then most boundary points of U (in the sense of harmonic measure) are also escaping. In the other direction we show that if enough boundary points of U are escaping, then U is an escaping Fatou component. Some applications of these results are given; for example, ...
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We study the dynamics of polynomials with coefficients in a nonArchimedean field L, where L is the completion of an algebraic closure of the field of formal Laurent series. We prove that every wandering Fatou component is contained in the basin of a periodic orbit. We give a dynamical characterization of polynomials having algebraic Julia sets. More precisely, we establish that a polynomial wit...
متن کاملClassification and Structure of Periodic Fatou Components
For a given rational map f : Ĉ→ Ĉ, the Julia set consists of those points in Ĉ around which the dynamics of the map is chaotic (a notion that can be defined rigorously), while the Fatou set is defined as the complement. The Fatou set, where the dynamics is well-behaved, is an open set, and one can classify its periodic connected components into five well-understood categories. This classificati...
متن کاملFatou and Julia Components of Transversely Holomorphic Foliations
In this paper we study foliations F on compact manifolds M , of real codimension 2, with a transversal holomorphic structure. We construct a decomposition of M into dynamically defined components, similar to the Fatou/Julia sets for iteration of rational functions, or the region of discontinuity/limit set partition for Kleinian groups in PSL(2,C). All this in tune with Sullivan’s well known dic...
متن کاملBoundaries of Unbounded Fatou Components of Entire Functions
An unbounded Fatou component U of a transcendental entire function is simplyconnected. The paper studies the boundary behaviour of the Riemann map Ψ of the disc D to U , in particular the set Θ of ∂D where the radial limit of Ψ is ∞ . If U is not a Baker domain and ∞ is accessible in U , then Θ is dense in ∂D . If U is a Baker domain in which f is not univalent, Θ contains a non-empty perfect s...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2016
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6739