Dynamics of entire maps
نویسندگان
چکیده
منابع مشابه
Dynamics of Entire Functions
Complex dynamics of iterated entire holomorphic functions is an active and exciting area of research. This manuscript collects known background in this field and describes several of the most active research areas within the dynamics of entire functions. Complex dynamics, in the sense of holomorphic iteration theory, has been a most active research area for the last three decades. A number of i...
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Let f : C → C be an entire map of the form f(z) = P (z) exp(Q(z)), where P and Q are polynomials of arbitrary degrees (we allow the case Q = 0). Building upon a method pioneered by M. Shishikura, we show that if f has a Siegel disk of bounded type rotation number centered at the origin, then the boundary of this Siegel disk is a quasicircle containing at least one critical point of f . This uni...
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The basic results of the iteration theory of rational and entire functions used in this paper are contained in the classical papers [10,11], in the survey [5] and in [15, Appendix III]. Let / b e a rational or entire function and let/" = /o . . . o /be its «th iterate. Denote by Jf(f) the set of normality of/ that is, the maximal open set on which the family of iterates is normal in the sense o...
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The Newton map Nf of an entire function f turns the roots of f into attracting fixed points. Let U be the immediate attracting basin for such a fixed point of Nf . We study the behavior of Nf in a component V of C \ U . If V can be surrounded by an invariant curve within U and satisfies the condition that for all z ∈ Ĉ, N f ({z})∩V is a finite set, we show that V contains another immediate basi...
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We give a new proof of the result that if f and g are entire transcendental functions, then f ◦g has infinitely many fixed points. The method yields a number of generalizations of this result. In particular, it extends to quasiregular maps in R.
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 1989
ISSN: 0137-6934,1730-6299
DOI: 10.4064/-23-1-221-228